Growing fresh herbs should work
as long as they can tolerate the salt
Much more than that becomes impractical due to space limitations. Where can you put the pots where they won't fall and break or be covered with salt
spray which very few plants tolerate. Unless you have a really bit boat
or devote every spare area to gardening there just isn't enough room to produce a usable quantity of most crops.
Also wonder if the tomatoes would stay on the vines when the boat
starts bouncing around.
I have to say that fresh fruits and vegetables were not easy to find in the Bahamas
. In a few of the larger towns there are regular US style grocery stores with fresh produce delivered regularly from the US but once you get into the out islands options are very limited.