Is it achievable? Yes. Will you be knackered at the end? Yes.
I did my PPL (including all exams & most of night rating) in 3 weeks. If the course you're offered includes exams in the price, I'd be tempted to take them there. The weather in FLA in Feb should be pretty good (it's not hurricane season).
I'd perhaps suggest adding on a week in order to make it less rushed. If you finish early, you'll have a weeks holiday
