This is one of the most complicated questions ever... the short answer is "no" but there are ways you can get connected. The thing to do is to contact Cable & Wireless to see if you can set up a temporary account. (your local service does not provide coverage in the Caribbean - even with roaming charges).
There are other avenues as well, I am told. Call your cell-phone provider and see if they can provide international coverage for you in areas compatible with their system.
Either way - it is complicated and expensive. I recommended doing what I do - visit the local Internet cafe in each port and send email, but first get yourself an account with HotMail!