Is it possible the study to the theory in the classroom, seat the exams in Florida and would it still be possible to finish the PPL course within 4-6 weeks?
Yes, it is possible, but the amount of time required to do the exams will to some extent depend on how much you know already. The new EASA rules dictate 100 hours of theoretical training before you can sit the exams. Whilst this may not be implemented immediately, at 8 hours a day that would absorb 12 days out of your allocated time. If you have the opportunity to get the exams out of the way before you go, I think most would advise you to do so. You are not eligible to take the flying skill test until all exams have been passed.