The better carribean schools might require a Bachelors degree. If you dont have one, and go to a 2nd or 3rd tier Carib school, you are setting yourself up for problems in the future. But it may not make a difference in the school itself.
It will not "cut down" any time in the Carribean. You'll have to complete the medical school curriculum. Besides, its a graduate degree, undergrad classes dont count for anything.
Do you need the BS/BA to do well? Maybe, maybe not. You'd need the 8-10 required premed classes to get accepted to med school. Completing a bachelors, and all the additional classes just might teach you how to study better. But that depends on how you learn. As far as the classes themselves - premeds don't really prepare you all that much for the med school classes. If you take biochem as an undergrad, that may give you a heads up.
One big issue is, when you eventually graduate, and get a residency, and then have to apply for your license to practice medicine - they are going to pull up every bit of education you've had since high school. Aside from the issue of being suspended/dismissed from college... The state licensing board will have their own requirements for how much Undergraduate school you must have sucessfully completed. Some states require 90 credits, some require a Bachelors. So, that can be an issue when you eventually are in 300grand in debt and need a job.