The Sprint TP2 is already unlocked for NON-US GSM use and is quad band + WCDMA 2100. So yes, you should be fine buying a prepaid GSM SIM for Jamaica... I dunno the situation in Jamaica but there are plenty of websites that you can search to find out what the GSM service is like there, what carriers operate and on what bands and roughly the rates. You may find deals on ebay and you can go to
www.prepaidgsm.net for a good forum that discusses these issues.