Isn’t acne “the red death?”
Rome would be wiped out by a flood of diseases the Marines would be carriers of.
I don’t see a Marine unit being entirely composed of men too incompetent and narrow in their thinking as to not realize the potential for biological warfare their bodies carry.
In fact they get vaccines against "exotics" like yellow fever, and would take anti-malarial meds even though these diseases are virtually unheard of in the US.
If anything, an unvaccinated Marine would be at risk for diseases the Romans might have or carry.
I don't think this would be an issue, like Columbus bringing smallpox to the Native Americans.
Thinking about this further, I can see perhaps TB being a problem for the Marines.
But what we have today is "multi-resistant" TB, brought in by third world hell-holes.
2000 years ago this would have been taken care of easily with streptomycin, because it was still effective.
A halfway decent medic would probably have the antibiotics they would need.
Penicillin would still have killed almost anything, because resistant strains didn't yet exist.