OP, something you haven't brought up, and perhaps because it is not a concern, is the cost of this program. Setting aside whether or not it is strategically a good idea to go to the Caribbean to do your prerequisites (I think this has been covered sufficiently by the posters in this thread and others), have you considered what sort of debt you would have to take on to attend this program?
If your are not financially independent, then I think this warrants serious consideration. It would be exponentially cheaper to do a formal post-baccalaureate in the U.S. if that is the route you would like to pursue. (Are you not considering formal U.S. post-baccalaureate programs because you don't have the grades to qualify? If so, this is another discussion entirely, and another reason you should stay stateside.) If you are open to a DIY route, depending on the state you live in and/or the relative availability of community colleges, it could be very cheap.
In any instance, setting the Caribbean debate aside (again, because I feel like it has been well covered) even if you have already decided you want to go to SGU for medical school, why take on considerable debt to do so BEFORE attending medical school (because SGU is expensive)? That is, even if you decide to go to SGU for medical school, there can be no financial justification to be made for the associated cost (flight, food, higher living expenses, etc.) of doing their post-baccalaureate program when there are much cheaper options.