Regardless of whether the BON requires it for NCLEX eligibility (and I can't speak for FL, but I've never heard of that in any of the states in which I've practiced over the years), every healthcare employer you encounter will require it. So, if that's going to be a problem for you, you may want to rethink your career goals.
I think you may be mistaken, you take the CNA certification state test after your CNA classes, not the NCLEX. The NCLEX is taken by Nursing school graduates, LPN's and RN's, which allows for licensing as a Nurse.
In any event, every job requires a drug test, so if that will be a problem then you should carefully consider whether or not health care is the correct field for your situation. People's lives and well being are in your hands as a Nurse, there is no time or place for drug use.
I'm not sure about the NCLEX, but I do know for a fact that anywhere you apply for a job, before you are able to work a drug test is mandatory. If you aren't able to pass, then I suggest that you find a new field. If it's something you are prescribed however, then you just have to be able to prove it. In nursing, you have peoples lives in your hands, and you have to be capable to take care of them in the right state of mind.