Specifically, if an invading fleet wanted to move from Naples to Rome, but the move was blocked by another fleet trying to move into Rome from the Tyrrhenian Sea, could a third player with a fleet in the Ionian Sea move into Naples, driving the invading fleet trying to move from Naples to Rome into the sea? Or is that just wishful thinking?
All the moves will fail; everything will end up where it started. From the rules, p9:
One unit not moving can stop a unit or series of units from moving. If a unit is ordered to hold, or is prevented from moving, and other units are ordered into its province, those other units can’t move. (It’s like a traffic backup!)