Florida is a closed primary state. I doubt they would reopen registration to allow Republicans to change their affiliation and crossover, since that would potentially allow Florida Republicans to vote twice.
I doubt they would either, but this would be an issue to be worked out in the bill authorizing a new primary.
In fact, I doubt the whole idea will go anywhere as actual legislation, but as a suggestion aired in public, it seems like a minefield for any Democrat - a minefield few Democrats will be allowed (by constituents or the press) to avoid.
I'd say they have to. The Dimwits are going to vote twice so why not? And FL has no problem with people changing their party affiliation before the primary and back after it.