They could probably do this with minimal resistance, even if the Romans could alert an army they were coming, it’s doubtful an army could even move fast enough to stay up with a modern marine unit.
They would walk in unopposed.
Then what? Defend Rome itself from the counterattacking legions? Largely cut-off from your fleet base?
I'd probably take Venice as my redoubt. Terrorize Rome with a Harrier pass (those puppies are LOUD). Make a heliborne demonstration. Mostly husband my resources near a secure harbor where my Amphibs can tie-up/anchor. Another possibility is Bari or possibly a base in Sicily. Sicily was alway in some state of rebellion. Always divided.
I might play the God gambit, I would fly in on a Harrier, set down in front of the Senate or Emperor’s palace and say I am Jupiter and kill the first one that doubts me. Then show them how I can call lightning (missiles) down out of the sky.
Then the Senate, and anyone else in power, can choose to defy me if they have the will.