Is there ADS-B Radar coverage in the Caribbean?

Generally speaking, the answer is no.  As you can see in Image 1, when using ADS-B the NEXRAD radar range is around 100NM offshore from Florida towards the Caribbean. Beyond that no Radar coverage is available via ADS-B.

It should be noted that ADS-B tower transmission range is between 60-90NM, based on your location, altitude, and type of receiving antenna.  Depending on these variables, you may not get offshore coverage to the extent pictured below.

Image 1.  ADS-B radar coverage off the coast of Florida.