I like lurking on the Alternate History forum, and I thought this idea is quite interesting...
Is it likely/plausible?
Not really. Pre-Panama Canal those islands would have had no value to the US. In 1868, IIRC, the then current dictator of the Domincan Republic offered to become a US territory and we declined. The Danes had been trying offload the Danish Virgin Islands for some time and we declined that too until the period we were preparing to add actual fighting to our participation in the Allied war effort in WWI and we became worried that Germany might make use of them.
Conceivably if there were a genuine independence movement in the French Caribbean we might have aided that.