I don't know for sure but I have a coast live oak (Quercus agrifolia) that I started from acorn and is now
15 years old, and know others in this area that have a few. They are native to CA and normally would not survive in this climate. The leaves reduce nicely. Since the florida live oak is native to your area it should at the very least survive. If it's at all like the coast live oaks when it starts sprouting new growth it's very fast, and has to be pruned almost daily. It's a great species for clip'n'grow.