Florida Baker Act

Most likely, yes. It may not prevent a purchase, but would certainly slow things down for a closer look at the circumstances and the outcome.
The Baker Act in and of itself does not prohibit you from purchasing a firearm.

ThebBaker Act allows authorities to have someone taken in for observation to determine if the person is a danger to themselves or others.

It's not automatically a bar to purchase firearms. Some people try use it on their spouses to get even if they are fighting.

If the person is determined to be mentally incompetent or is committed to a mental facility, then you will have issues.

Here's what your FDLE says about The Baker Act and firearms purchase:

That tinfoil hat you should be wearing will shield you from the effects of the Baker Act.

I know two wonderful, real bakers in my area, nice people.

I'm a reserve deputy sheriff and serve a couple of nights when I can.

One of the bakers owns a local Dunkin Donuts, and always offers us hot donuts and coffee.

The other guy works at a local donut shop.

Both fellas always offer us hot donuts and coffee when we're shaking locks in some little country Texas town in the county.

Bakers have always been cool....