Germany not wanting to trigger a general war with Britain & France, elects not to invade Poland, but moves Southeast either into Hungary or Yugoslavia. Would England and France fight for either of these countries? Would Poland declare war to aid either of them, or could it be bought off as it was with the occupation of the rump of Czechoslovakia? Could Germany aquire a 'Balkan' empire without triggering a general war? Could Russia continue to be worked with by Germany?
Considering that when Germany annexed Czechoslovakia and did three things (1. Annexing the west completely into 'Greater Germany' 2. Establishing the east under a puppet government and 3. Giving the Presov region and nearby to Hungary), I doubt France and the United Kingdom would help Hungary had they been invaded, considering that they were already 'in a relationship', I guess you could say. Hungary was not guaranteed independence by the Allies, unlike Poland (which is why the UK and France declared war on Germany on Sept. 3 1939), which means the two democracies would've done very little - if most, probably along the lines of a second Munich Agreement or something along those lines - to try and appease Hitler yet again.
Really, why would Germany invade either Hungary or Yugoslavia. Both were pro-Germany at the time. Yugoslavia avoided joining the Tripartite alliance by overthrowing the government in 1941 which resulted in a German invasion. Even Greece had a dictatorship government as well. I don't think that Hitler wanted trouble in the Balkans at any time due that would endanger the Romanian oilfields.
You are correct Hungary is pro Germany, and so too Yougoslavia at this point. Germany, or rather Hitler, did not look upon allies in the same way as most. Hitler's objective was a 'living space' and the creation of a Empire. If he could gobble up one or more east-european or balkan states without triggering a general war and bring the natural resources, industry, economies, and food production into the greater reich, how would this improve Germany's position? Could Germany go so far as as Rumania and Bulgaria, but not Greece? Could Hitler create his empire out of the Balkans without triggering a do or die war? Would giving Russia a free hand in Turkey be enough to buy off Stalin?
I think as far as Turkey goes, the potential for usefulness in the inevitable later conflict (despite the actual neutrality in reality) as far as the middle east is concerned would make it unthinkable that Stalin would be allowed to move in there - quite apart from the fact that all moves in this area, regardless of any minor fulfillment of Hitler's motives, would not provide the lebensraum and resources needed without Poland and significant parts of Western USSR. Another fact to consider is that taking the balkans before letting the Italians have a try would have alienated Italy, and Romania had ties to France almost as strong as Poland, albeit less formalised. Hungary was always considered a 'historical' part of the Reich, and by nature of her location and near undefendable borders to the west, could never be anything other than a Reich puppet except perhaps a pro-axis neutral.
Well, at least Germany need to make sure they don´t end up in a two-front war, i.e. they need to give up something to Stalin that will keep him satisfied. I recall that Hitler was trying to get Stalin to "attack" in the India direction, but to me it seems Stalin was more interested in making Leningrad safe ( Finland , Baltics ) and in the southern sector the Bosporus straits. And definitely Hitler to me was not going to let the USSR get hold of Turkey or get close to the priceless Ploesti oil fields so something else had to be offered. Hitler was already possessed in starting the war practically, and was ready to make almost any kind of agreement with Stalin. And if anything, the German generals accepted that Poland was enemy no 1, Hitler needed not explain why, they all seemed to think Poland should be crushed. Then not sure if Poland would be interested in helping Yugoslavia if Hitler should be heading in that direction but definitely Hitler´s flank would be open to the Polish army, if Hitler was wishing for a non-fighting solution. But to me it seems Hitler never wanted to go "south" because operation Marita only took place due to poor Italian offensive achievements there and the unexpected 27 March 1941 coup d'état against the Yugoslav government.
The challenge to a alt. history what-if is that they usually begin with a 'rational' Hitler, which of course leaves us on shaky ground at the start. The viability of a German move, first into Hungary and then into the remainder of the Balkans rest on the answers to a few questions as I see it. Question 1, Will Britain-France-Poland fight for Hungary in the fall of 1939? Spartan like you I do not think Britain and France would have the stomach to fight for Hungary, and I suspect Poland could be apeased with a few strips of land as they were with Czechoslovakia. (Funny how Poland got a pass on that). In this case a walk over for Germany. If however the Allies elect to fight we get a slightly different outcome. It will still take a year, perhaps 2 before Britain and France can attack Germany proper, and both Poland and Hungary will fall long before that happens. In fact I suspect a resolution to Germany's 'Eastern' campaign in 1939. The cost would be higher, perhaps twice that of a Polish invasion alone. Serious, but not crippling. Germany faces Britain and France a little weaker perhaps, but with greater political cache for its eastern victories. The Anglo-French armies are beaten in 1940 as they were historicly, but the cost is a little higher for Germany. The somewhat greater strain on Germany might have the benifical effect of cooling Hitler's arder for a 1941 invasion of Russia. Since it no longer matters what Britain-France think, Germany could spend 1941 gobbling up Yugoslavia, Rumania, Bulgaria and Greece. A 'rational' Hitler would pause there to create his Greater German Reich and bring all the resources together for a final showdown with Stalin after a few years time. If the oppertunity to attack Russia does not present itself, Hitler still has a great empire. Question 2, Will Hungary Fight? If she has Allies, without question, but what if no one comes to her aid? Hungary with no one to back her might capitulate without a fight as Czechoslovakia did to preserve its people and cities. If she does capitulate then Hungary's arsenal's, industry and infrastucture are transfered intact to Germany. Another bloodless victory would burnish Hitler's reputation. Any resistance, would be short lived and futile. Then in the spring 1940 first Poland, then Britain-France summer-fall 1940. Question 3, What about Russia? Clearly Russia had ambitions to create buffer zones around its core nation, and was not above using force to get these. They, though secret treaty's and protocal's helped Germany carve up eastern Europe, so there seem's to be a deal or two two be made here. Turkey is a case in point. Who is there to prevent Stalin from moving into Turkey? Germany never expressed any serious middle-eastern desires, and only got dragged into the area due to Italy's inability to protect thier empire. Britain and France would not want them there to be sure, but after 1940 what could they do about it? Would Britain declare war on Russia over Turkey, knowing that they alone could not defeat Hitler as it was? The US will not fight over Turkey, so who remains to stop Stalin from fullfilling a long cherished dream to have unfettered access to the Med. Question 4, What about Italy? Would hurting Il Duce's feelings be such a bad thing in the end? I was struck by a line in the 10-part history of WWI from a few years back. A German officer commented that Imperial Germany's alliance with the Austro-Hungarian Empire was like a man being shackled to a corpse. Nazi Germany would learn that there are worse fates, such as a man being shackled to a zombie. A corpse, while a dead weight and a bit smelly, does not stagger off in a odd direction for no logical reason, forcing you to change your plans to accomodate thier erratic behavior. When Il Duce signed the Pact of Steel with Hitler, he warned that Italy would not be ready for an aggressive war until 1943, '42 at the earliest. This was an overly optomistic prediction. It truth Italy would never be ready to fight a modern war considering both how their weapons were procuered and produced, and how the Italian soldier was trained to use them. When Germany invaded Poland Mussolini begged off from fullfilling his agreement, and Hitler let him do so because it was understood that Facsist Italy was a paper tiger at best. When he did declare war on Britain and France, the Duce demanded massive amounts of coal, oil and minerals that were used to produce absurdly small numbers of unforgiveably worthless weapons. Weapons put into the hands of an indifferently trained and unimaginatively led military. Germany could have produced more weapons, of much better quality with those same resources. If that was all it cost Germany it would be bad enough, but within months Hitler would send ever increasing numbers of men and machines to help Il Duce lose his war at a slower rate. We could debate whether these men, equipment and resources would have been decisive elswhere, but what I feel is not debateable is that long term Germany gain nothing of value from its alliance with Italy. Far worse the Italian Alliance gave the Anglo-Americans 2 plus years of the best live fire training they could ask for. The allies fought an opponent not able or willing to defeat them, over ground not strategic to thier victory, learning what tactics and equipment worked, and which did not. So that by 1944 when they were ready to take on directly Hitler's Fortress Europe, they had a well trained, equiped and oiled war machine to do it with.