Looks like it is most of the time. One thing to keep in mind is that November is still hurricane season, so if a hurricane is nearby, Scuba diving is impossible.
It is going to be as safe as any other time going SCUBA diving. One particular month does not make SCUBA diving dangerous. As long as your guide knows what their doing, you will be fine.
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Yes. Many migrant species such as Spanish and king mackerel are there in fall in numbers.