Nope, the programs are mostly school exclusive. You can either try further down south (South America, anyone?), Mexico, or wait for someone to say something about a accredited program.
The education in the Carribean can vary. They can mix the use of local teachers and foreigners. Try a Canadian school, they're pretty cheap and solid. But, if you want top notch education, but expensive, try the UK. The middle ground (in my eyes) would be the US.
If you weren't referring specifically to the Carribean. There are schools with percentage numbers of premed students that actually get into the med school that they're associated with.
Lastly, licensing requires 60 (2 years)/ 90 (3 years) in US/Canadian school.
But, some States say equivalent too. So, watch out for that.
That's all I know.
Hope I answered your questions adequately.