All Encompassing Goose: I often consider doing this too when playing A&A Europe 1940 2E “Standalone” (not global 1940). I have tried it several times as the allies as has my son (with me playing the Axis).
Here is what we found:
1.) You can take Greece as UK round 1, you can do this even if you commit the remainder of your ships in the Mediterranean to the Taranto raid. Usually, it makes the most sense to bring 1 infrantry and one tank to make the foothold in greece the strongest, but doing this weakens Cairo’s defenses quite a bit.
There is no opportunity to re-inforce greece before Germany turn 2, so best case, Greece will have 5 infantry and 1 tank available for defense.
2.) The net effect of taking Greece on UK round 1, based on several playthroughs, is that best case, you slow down Germany’s push toward Ukraine for a turn or two as the german player feels they can’t afford to leave Greece uncontested. Germany is usually able to take Greece on Turn 2 with moderate losses depending on the forces they commit.
I haven’t run into it, but I am sure there can be an extraordinary battle roll in the UK’s favor such that they keep greece past Germany turn 2 and they can reinforce it with fighters, etc.
But most of the time, the entire endeavor amounts to slowing/delaying germany’s southern thrust into russia by 1 turn, maybe 2.
In the real WW2, UK did try re-inforcing greece from egypt and germany conquered greece anyway (see:[https://en.wikipedia.org/wiki/Operation_Lustre](link url))