As an innovation, the R4M certainly has had its impact. Post war it is likely one of the most copied ideas for unguided munitions there is. Its successors are still going strong in the realm of ground attack.

But, in terms of WW 2 the R4M was intended first as an Air-to-Air weapon. Coming into service very late in the war there is little evidence of its effectiveness in this role. As I understand it, the rocket is attributed just one kill early in 1945.
Post war, the US more or less copied the R4M as the FFAR 2.75" rocket. During the late 40's and 50's this weapon was in widespread use as an AAM. It reached an extreme on aircraft like the F-89 where some models carried over 100 and could blanket a square of airspace bigger than a football field.
By the late 50's however, the FFAR had fallen virtually out of use completely as an AAM; replaced by guided weapons and a new generation of rapid fire cannon. Having seen little, if any, actual aerial combat it is a bit difficult to rate the FFAR in effectiveness as with the R4M.
What I have been able to uncover about its performance was that the velocity was too low and the rocket too light to be really accurate in operational use. Hence the need for lots of them to be salvoed to get a hit. Both gravity and wind / air motion had substancial effects on the FFAR.
The R4M likewise was no doubt similarly effected. The Germans countered part of the gravitational effect by putting an 8 degree elevation on launchers relative to the aircraft's line of flight.

As a WW 2 weapon I think the R4M had real potential as a bomber buster. Although it had a claimed range of 1000 meters I would think that a 500 meter firing range would have done better in terms of both ensuring a hit. Pilots could have very likely scored on a bomber using this weapon from that range given a salvo of about 20 to 30 rockets. A pilot could also have been easily trained to make high side head on deflection passes against bombers to make defensive fire less effective, something that the average pilot would have difficulty doing with guns alone.
The big advantage for the Germans is that their two mainstay fighters could have carried 20 to 30 of these rockets for a total weight of about 350 lbs load. There would also have been a slight drag penality involved. But, this is offset by reducing the gun armament to just sufficent for defense against escort fighters.
With each defending fighter making a single pass and then leaving the combat area the Germans could have minimized flight times and exposure of their fighters to the bomber escorts.
If one assumes even low kill rates of say, 10 to 20% of the firing passes this equates to a substancial number of losses. When the Germans were putting up several hundred fighters this means that as many as 20 to 80 bombers would go down. The upper end of this scale is beyond acceptable losses. The R4M just might have succeeded; at least for a time.