Caribbean medical schools?

Yes, they are frowned upon, although I guess Ross might not be as bad as the rest.  

In the US Residency match, you'll be competing with practicing physicians in other countries for leftover spots after the US MD and DO students match.  It is unlikely that you'd get a spot in a competitive/lucrative specialty or a prestigious/desirable location (those get snatched up by US grads) unless you are a well-connected superstar, and possible that you wouldn't match at all.  

If you do get matched and complete your training, passing all necessary exams, then you can practice in the US just fine.  The hard part is getting a training seat.  

Usually the recommendation is to go American DO over Caribbean MD.  US DO students usually fare better in the residency match than do Caribbean MDs, and have a DO-only match as well to rely upon.  Debt/loan burden may also be a consideration.