Do contact your cell phone provider and ask for the latest and greatest. You may find that you get a signal and place a call, but you could get a surprise when the bill comes. Different companies have different rates for different locals. The rate can even vary from one plan to the next with some companies, so one person's experience may not match yours.
The other thing that can happen is that your phone may need an update in order to work. On our last trip we called Sprint a couple of weeks before we went, they had just added service to St. Thomas, but phones required an update to work there. We were able to get our phone updated before we left and it worked fine. My sister also had Sprint, but did not get her phone updated and it didn't work in St. Thomas.
We just called before leaving with a list of ports. Sprint was able to tell us where we would have service and whether or not roaming charges would apply in each port based on our plan.