Many, many carib IMG's are able to get a spot in the US for postgraduate training.
SGU posts their placements online. I believe ross does the same.
A few points:
1. More competitive programs will be harder to get. Orthopedic surgery, ENT, plastics, rads, derm, etc all are very competitive and Carib grads are at a distinct disadvantage. This can be overcome by outstanding USMLE's, research, etc, but is difficult.
2. IM, FP, Peds, etc are all very reachable. The top programs may be out of reach, but there are (currently) plenty of spots for good Carib IMG's.
3. Your USMLE scores are much more important than for US grads. Make sure you do as well as possible.
4. Fellowships in IM are getting more competitive. I'm seeing some IMG's have more trouble getting one post residency, even if you attend a good residency program.
5. Some Carib IMG's do not match. I expect these are poeple who had less than stellar USMLE's, or tried for overly competitive programs/fields. Still, it's a risk -- if you don't do well on your USMLE's, you might struggle in the match.