A couple things IMO on this question...
1) I believe the Allies would have had to attemp to attack Italy from Southern France via Corsica and Sardinia ( I believe they had plans for invasions of those called Operation Firebrand and Operation Brimstone).. then work there way into southern Italy, no way where they going through the Alps..
2) The Axis forces would have probably gone through Syria into Turkey and what is now Georgia to attack Southern Russia (A fourth Front, to go with Barbarossa) and since Romania was an Allied to the Axis I believe the rest of the Mediterranean would have fallen (Greece, Turkey, etc.)
3) The Question would be Saudi Arabia would the Axis have gotten their hands on more oil...
4) The Italians would have been in the war longer
But in the end I believe the might of Russia and the Western Allied Forces would have prevailed, but it might have extended the war a few years