What would have happened if the Roman Empire had fallen back to Italy?

That was theory and in fact an ideal but unrealistic. The reason for that was civil wars. Rome fought a dismally long list of civil conflicts that used up resources and devastated the countryside and reduced the military to becoming filled primarily by foederatti. These were comprised of barbarians (who by this time were not their father's barbarians) and auxillary forces with lax discipline and even worse patriotism. Rome bled herself dry in wars against herself. To fund yet another army taxes were increased and peasants and pretty much everyone who wasn't someone would make themselves scarce around tax time. Even so Rome was so well organized (the benefit of centuries) that it's institutions creaked along for a surprisingly long time before true collapse and that was in the west mind you. The Byzantines still had a thousand years to go ahead of them. Africa was the breadbasket and Rome had a million mouths to feed.

Could it have been done? Sure. But who was going to let so and general become emperor when such and such general had an even larger personal army devoted to raising him to the purple? And this and that's legions were marching towards Italy and he has always wanted the throne as everyone knows! Armies generally fought for their commanders who were usually rich and could pay them when booty wasn't forthcoming etc.