This has been discussed over the years on various forms. Too often such discussions start with the understanding that the Soviet Union wouldn't be defeated. From that perspective, any Italian forces sent to Russia would be wasted. So what are the real issues for Italy?
I personally believe that sending Italian forces to Italy was a poor strategic decision by Italy. That being said, I am not sure any forces freed by a different decision could be effectively employed in A.S.
There are some positives for Italian participation in Russia.
Success would provide a greater degree of strategic freedom for the Axis than they enjoyed in the summer-fall of 1940. Defeating the Soviet Union would mean that German forces would be freed to operate in other theaters (such as the Mediterranean). There is much to be said for maximum Axis effort against the USSR.
This must be balanced against the realities of the German and Italian decision-making in 1941.
-Germany had already decided to invade Russian without gaining Italian concurrence/participation.
-Germany believed that she alone could defeat the Soviet Union.
-Italy had already committed itself to the Mediterranean and Balkan theaters.
Russia offered many of the same logistical challenges as seen in A.S. Long lines of communication, poor road/railway system with low capacity, mud instead of sand, rivers instead of depressions. etc. The only difference was scale. The breaking point was significantly higher in Russia than A.S. (100s of divisions in Russia vice 8-10 division in A.S.).
If the material sent to Russia was instead available for use in A.S., what would really change? Clearly more Italian units could be motorized, but the cost would be increased fuel/parts requirements. The combat material itself wasn't of greater value (more 47/32 c.c. or carri L6) than what was already available in A.S? The mod 75/97 c.c. would have been a plus in A.S., but would the Germans still provided them to Italy (they were only given to the 8ª Armata)? A few more of the excellent cannone da 149/40 would be available, but I can't think of anything else that wasn't already being used in A.S.
A significant amount of material was already being held in Italian ports awaiting transport to A.S. Are these piles to grow bigger without an increase in shipping? Nothing sent to Russia materially aids addressing the Malta problem.
A question is whether Italian forces could have been better use to replace garrisons in France/Balkans to free up additional German forces for Russia.
Pista! Jeff