In his book Lost Victories, German Field Marshal Manstein stated that solving the crisis of the winter '42/'43 that resulted from a botched strategic campaign planning in the summer of '42 and became famous for the battle for Stalingrad and ended in the battle for Charkow was not a step to victory but marked the turning point from where on a military decision resulting in a victory was no longer feasible. Instead, the goal must be to achieve operational independence for the summer of '43 to beat and bleed the Russian army dry to achieve a good position for a peace negotiation. Obviously that goal was not achieved, even ignoring the fact that the German leadership would never have negotiated.
So this book has received a lot of criticism, but I think it does reflect Manstein's view on military matters or at least is consistent with other books written on that subject.
By the start of '43 even when the German army stood deeply in Russian territory, believing in a victory was foolish. Their military best case scenario was coming to favorable peace terms. Obviously you will not find this in official documents. That would have been "defeatism" and the offender would have been shot.
In the winter of '42/'43 the Russian army demonstrated that they were able and willing to defeat German armies in large scale operations and that the German army - just as in the winter of '41/'42 - had stretched to far and had suffered horrendous losses due to this mistake.
So yes, having more than this one front for example in Africa or later in Italy or even later in Normandy helped to keep much needed personal, equipment, transport capacity and air-power away from the eastern front.
I think it's safe to say that as an end result, more troops with better equipment under the same command and with the same strategic goals might have made a real difference in '41, and certainly would have cost the Soviet Union a lot more in lifes even later in the war, but by '43 and certainly by '44, the lack of manpower and material on the eastern front was a result of losing, not the reason. There was no realistic option to win the war against the Soviet Union by early '43.
The allied fronts certainly sped up the loss and helped to defeat Nazi Germany. But according to German military leaders account's, the war with the Soviet Union was lost anyway. It was only a matter of time if you did not believe in "Wunderwaffen".
For a first-hand account on how badly the Wehrmacht was mauled in '42 and up to the end, I can recommend the book "Vergiss die Zeit der Dornen nicht" (engl. title: blood red snow) by Günter K. Koschorrek.