I haven't lived in FL for more than 20 years so I can't be very helpful. Based on my limited knowledge, you should be able to harvest as long as you keep the soil moist enough (which can be hard in hot, sandy soil) and the plants are affected by the heat. You should have better luck getting an answer in the vegetable forum, and by using cucumbers in the subject line.

Here is a link that might be useful: Vegetable Forum

Why wait till Sept. to plant, Plant now and you should make it, but Sept. is a gamble on 1st frost getting it.