What would have happened?

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"Better a pint of sweat than a gallon of blood."
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Thanks to swfan for my sig

And, what exactly are you proposing to power this aircraft with? The Junkers Jumo 004 turbojet was not even a prototype at that point. Ohain's HeS 04 - 06 had severe problems particularly with fuel leaks and far less power.
A prop driven version would have no doubt been difficult and it is very likely that its performance would not have warranted its production.

I suspose he is assuming the appropriate engines are available.

Unless the Luftwaffe changes its doctrine they will be using this plane as a tactical bomber, like the He177 was abused.

Assuming the doctrine is changed. Maybe Wever is not killed in a accident, then enough of them have to built to make a difference? How many He111, Ju88, or FW 190 are not produced so the HO229 are built?

The US & Britian had to build thousands of heavy bombers of this class in order to make a noticeable dent in German & Japanese warmaking ability. Is there any concieveable way the German aircraft industry can put even one or two thousand of these aloft?

One huge advantage the US & British antiaircraft defenses had from 1941 was the proximity fuze. These proved devastating vs agile Japanese tactical bombers. I'd expect the less manuverable heavy bomber would be easy meat for the radar fuzed AA ammo of the Allies. Losses of the HO229 would rival that of the Allied heavy bombers.

Ok, the Germans deploy jets in 1941. The US and British respond by pushing up their own jet development. As the US had already produced a six million square foot plant to build jet engines they didn't have yet (yes, GE did this in 1941) the facilities exist to manufacture huge numbers of jets in the US.
What would certainly happen is that the US and British would muddle along for much of 1942 and then simply swamp the Germans with equal or better jet fighters and bombers in huge numbers by 1943.
Technology is at best a very short term advantage of only small difference in war. The more important and dangerous a new technology is to an enemy the quicker and more effectively that technology will be countered. This is certain to be the case here.

And who knows, maybe the Russians could have gotten this beauty up in the air before it first maiden flight on may 15, 1942.

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The war against Russia will be such that it cannot be conducted in a knightly fashion. This struggle is one of ideologies and racial differences and will have to be conducted with unprecedented, unmerciful and unrelenting harshness. -Adolf Hitler

Knowing the Soviets, they likely would have gotten a Dewent from the British and / or a GE turbojet in short order via Lend-Lease and simply built something like the MiG 15 by 1944 along with earlier jets like the Yak 11.

Those damn Russkies!

__________________
The war against Russia will be such that it cannot be conducted in a knightly fashion. This struggle is one of ideologies and racial differences and will have to be conducted with unprecedented, unmerciful and unrelenting harshness. -Adolf Hitler

Opps

I mistook the HO229 as a refrence for a heavy bomber project.

Heres a link to a long discussion of the relative merits of the various German & Allied jet engines of WWII. A pair of engineers are the primary contributors & the technical level of the posts way out there. My take is had jet aircraft been operational the Germans would have been in even worse condition due to the shortage of critical metals for extending jet engine life.

http://www.ww2incolor.com/forum/showthread.php?t=4648