Interesting TL, although I don't know how much tolerance the US would have for Italian interference in South America. That was traditionally OUR place to mess with.
Plus, I would imagine the "Rome Pact" would be REALLY unpopular in much of the US body politic due to its involvement with apartheid South Africa.
Also, what does the post-Salazar Portuguese government do with Mozambique and Angola? It was the decolonization of those states that gave anti-Rhodesian guerrillas more foreign backing and sanctuary, enabling them to force the white government to the table.
If something similar happened in TTL, it would be egg on the Rome Pact's face, especially since the establishment of Zimbabwe would in turn give guerrillas more sanctuaries on apartheid South Africa's borders.
Also, given the time it would take for a Rome Pact force to sail to India, the Indians would have plenty of time to build up and await the coming of the enemy. And a surface fleet would be vulnerable to nuclear attack.
A more dramatic end to fascism would feature the nuclear destruction of the Italian fleet off the Indian coast and the destruction or capture of the Italian forces that had already landed by prepared Indian troops setting off a popular uprising against the fascist government, much like the British victory in the Falklands War brought down the Argentine junta.