However, without forces in the Mediterranean (and possibly the Balkans) I think it is possible the Germans might have had sufficient resources to win in Russia.
Not necessarily. On the one hand, it's true that Italian operations in the Balkans (and North Africa) drew in some significant German forces which might otherwise have been used against Russia. What has to be considered on the other side of the scales, however, is that Italian neutrality would have made things a lot easier for the British and (later) the Americans. Britain would not have had to fight its minor campaign in East Africa, nor its much larger two-year campaign in North Africa. Naval control of the Mediterranean by Britain would have been easily maintained, instead of requiring a great deal of effort (such as the defense of Malta). Furthermore, Italian neutrality and the non-existence of a Balkan campaign by Germany implies that Greece would not have been occupied by the Axis. Greece and Britain were friendly. The combination of an undisputed British presence in Egypt, British control of much of the Mediterranean, and the presence of a free and friendly Greece on the southern European coastline would have created an early opportunity for the Britain and/or (later in the war) the Anglo-Americans to invade continental Europe in strength by taking advantage of the fact that making an unopposed landing via a friendly/allied country (in this hypothetical case, Greece) is a lot easier than invading a hostile country (which Italy was in real life when the Allies invaded it in 1943).