It should work, if your phone was purchased in the last several years - Sprint roams on Digicel in Jamaica, even for data. That said, it will be expensive to roam and may be much slower. If they're short calls, infrequent texts, and you don't use the web too much, it might be manageable. Check with the company for specific roaming costs, so you can see exactly how expensive it is. Personally, I think you're better off staying in touch over the web on the resort's wifi and computers. If your phone is wifi-enabled, you should be able to use its non-phone and non-text features that way, too. Just shut off voice and data roaming features so you don't come back to a surprise big bill!
One year, we just made calls with the digicel roaming charges, and found it very expensive ($2.99 a minute if I remember correct and .50 per text). Next time, we called our provider and upgraded to international roaming for a month, which was something like $15.00 extra. We made all the calls and texts we wanted, then canceled the international roaming when we returned.