Yes you will have coverage, it will be international roaming charges and will be
very expensive(Voice Pricing
: $2.29/minute per sprint.com). Visit a local phone shop there and buy a local SIM card and also a pre-paid calling card for voice usage. You will definitely want to keep your data turned off unless you leverage wifi hotspots, as the data charges will mount significantly as well.
If you are going to be in Nassau, look these folks up -
Island Cellular