Maybe, maybe not. Here's how it plays out:
He's going to be running for Senate. Say he signs the bill. Now he's pretty well lost his endorsement from the NRA (as well as Gun Owners of America) in the Senate race and antagonized not just gun owners in Florida but across the nation who will see him caving on gun rights as a Senator. He will lose his Senate race either in the primary or the general, but he will lose. Watch for the avalanche of memes and bumper stickers to flood the market during the race.
He doesn't sign it and lets it languish on his desk without comment or just says there's something in the bill he doesn't support and tells the Florida Senate and House to send him a new bill. It drags out, nothing gets passed and things stay as they are. Progressives go crazy, the NRA and GOA cautiously endorse Scott for Senate and he might win the Senate race in a squeaker.
If Scott signs that bill he can kiss N FL goodbye in the senate election. Its major hunting territory. I’m from Jax. Its gun country.