Net gain from no Italy wouldn't be that large - you'd be exchanging 3 Italian divisions from the CSIR (about 60k men) in 1941 for something more akin to Spain's Blue Division (20k men). And the CSIR would almost certainly not be expanded into the ARMIR (235k men) in Summer 1942.
Also the British now have much more breathing room to work with, so assuming they don't do anything with their now unoccupied divisions seems silly.
No delays to Barbarossa probably doesn't mean the fall of Moscow or Leningrad - the simple reality is that the Wehrmacht was at the end of its logistical tether by the time it reached the outskirts of Moscow in OTL. I could certainly see a battle for Moscow, but given that it'd comprise mostly of hellish urban combat I doubt the Nazis would end up successfully taking the city.
The thing is that Great Britain does not know if Italy will enter the war at a later stage so they will have to keep forces in place in North Africa and they will probably reinforce their Greek allies.
Even with Italy not being an active participant massive convoys through the Mediterranean and past Gibraltar is probably ill advised.
As for the starting point of Barbarossa in May instead of June, as the original plan called for, may give the Germans a chance to interrupt Soviet attempts to move the industry behind the Urals. In particular the production of the KV.
While the KV did not have the same potential to grow as the T-34, in 1941 it was the KV which gave the Germans difficulties and not the T-34 as popular culture likes to portray it.
Given how close to the edge the Soviet Union came that first year, that one month extra for the German offensive may delay/blunt Soviet responses. OTL the Soviet union could only bring in last minute supplies to the besieged Leningrad because the lake froze over.
Again, one more month to play with might lead to the fall of Leningrad.
It is a point of discussion, but there are sufficient scholars who believe that the delay in Barbarossa was the single most important reason why Germany did not capture Leningrad and Moscow.