Would the number vary if we replaced US Marines with Royal Marines, Korps Mariniers, Amfibiekåren etc?
Meh, when they have bathed in whats left of the Marines, perhaps, but otherwise the colour of the legions tunic does not matter, what matters is the only ones who ever defeated them wholesale were Germanic Tribesman, and seeing Marines dont speak German or carry axes, I see them failing...
Everybody knows the Army would be better suited to take on this mission, those guys really pack a punch.
One has to distinguish between 2 scenarios:
1. "Marooned Marines"
A bunch of Marines gets send back in time by accident (e.g. US invaded Switzerland, they turned the LHC on).
Then the best thing for the commander to do would be to avoid contact and conserve ammo and wait for the folks back home to figure out how to get them back.
2. "Invasion from the future"
Due to some disaster in the future (alien invasion or so), humankind comes up with the idea to avert it by giving humanity a 1000 years head start.
The Roman Empire of lets say 100-150 AD had all the requirements for industrial revolution. They just didn't need machines because they had slaves.
So a marine unit plus scientists et al are sent back to invade the future, change history and skip the entire middle ages.
Pizarro and Cortes were not alone they had on their side powerful allies (in fact several thousands of indian auxiliaries)And 2,000 vs a whole empire?
Pizaro and Cortes would have laughed at these odds.
Moreover they fought against highly centralized empires : cut the head (kill the Emperor-God) and that's (and was in reality) over
Roman Empire is less centralized : Several Emperor were killed during history and the Empire prevailed without problems
Hum with all due respect you better check it again; In fact look at Noche Triste and the resistance during the Siege of TechnocticlanThey showed initial massacres had a powerfully chilling effect on allies and civilians.
In the first event, despite the atrocious amount of caualties Aztecs slaughtered the spanishes (who were here, alone without their non-mexica allies)
See my post aboveMarines would be flush with new friends in the form of disgruntled conquered barbarians who would use the timing to rise up
Cortez was able to allie with locals because he had translators
Pizarro was able to communicate because he had translators (The Malinche comes to mind)
Moreover both were successfull because they came during or just after a period of civil unrest and political instability
That may be a key for success for a Marines unit if they pop up at the right time
And they need to land close to Rome indeed
But again they will lack translators (more than probable) and they won't be able to capitalize on a religious belief like did Pizarro and Cortez
Romans were not so supersticious and knew to indentify a Human even if it looked strange (on the contrary to the Aztecs and Incas)
Finally they were pretty much accustomed to fight new strange opponents from half naked barbarians to silk covered persians and moustache bearing scythes
They new what looked like an African or Caucasian man (maybe even an asiatic depending of the period)
So don't expect a meso american style bowing
As i said the first legion encountered would be annihilatedHow demoralized would Roman soldiers be after meeting the bullet for the first time? How could they possible calculate how many bullets Marines had with them? 40mm grenades? Hand grenades? machine gun belts?
My remark about baionnette was intended once the ammo would be expended
Because in a scorched earth and guerilla policy that will ensue the annihilation of the first regulars forces, finally you can expect to fall bingo ammo pretty quickly
Now the final outcome i see however would be as i said : auxiliarisation proposal after the first Marines victories
Romans were cleaver. Impressed by the did of the MAU, they would certainly ask them to join the Empire. That's here where the history can diverge : either the Marines refuse and are doomed to annihilation except if they are poping up in Rome (and even then, the Empire is still huge and decentralized enough to carry on the fight) either they accept and are integrated and assimilated within the Roman structure.