Roman tradition specified that no Roman legion could be admitted within the city walls except in rare specified circumstances such as a triumph. Bringing troops into the city was considered treason to the state.
While this tradition may have been breached in the later stages of Empire, the fact that Roman Emperors were sometimes assassinated by their Praetorian Guards and the reins of governement turned over in a coup should prove that regular legions were not quartered in or near Rome to protect the Emperor.
I suspect it would be relatively easy for the Marines to off the head of the snake.
A heavily armed and well trained unit like a Marine expeditionary force could easily destroy any armed military units an Emperor might have in Rome. The majority of Roman troops were always out in the provinces, not near Rome.
Outlying legions in the provinces would take months to come to the relief of Rome and by that time it is likely that a new government would have been established.
As far as the population of Rome taking up arms to protect the government, the fact is that a very high percentage of the inhabitants were slaves with no reason to have any allegiance to the government or any particular head of state. In fact, the Marines might find it very easy to recruit spies and warriors to aid them who were familiar with the city and Roman tactics.
I agree, the marines could go directly into Rome and take it over or level it.
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.