Congrats on getting it installed. Got pics?
Regarding the structure, you're giving Broncos too much credit. Sheet metal it is, and mostly just one layer over most of the truck. The only places where it's double thick are where Ford could not figure out a less expensive way to spot weld two panels together.
So no, the floor is just one layer over most of it's area, with things like strips and corrugations for rigidity. But not for strength for mounting a roll-bar, since Ford did not offer one. Or likely not even think one was going to be used by the owners.
Then again, maybe someone was thinking along those lines since that one area just in front of the rear wheel wells is flat without corrugations?
Luckily, as it turns out most of us have never put the roll-bars to any kind of a stress test by rolling over. Because over the last sixty years most of them were indeed as you suggest, just bolted straight to the floor. Some without even utilizing larger than normal washers to spread the load. But the issue was known from the beginning, so some of us did practice better mounting strategies. And some, not so much...
Some used larger washers, some of us used reinforcing plates, and some actually went the whole way and made custom lower mounts to connect the roll-bar feet to the frame of the vehicle.
And then there were the custom cages that had floor braces that mounted the seats and seat belts to the cage, rather than to the floor. The thinking being that if the cage detached from the body, the passengers stayed with the cage. Not sure if that's actually a better mousetrap, but it does make a certain sense.
Then you still have to contend with your head bouncing around during an accident and banging on the vertical tubes of 90% of the roll cages out there. Having that main tube right behind your ear is not exactly the best placement. Looks good, but you hope you never have a bumpy enough ride to conk your noggin on the bar. Or worse still, an extension bracket for the shoulder harness!
My recommendation would be to at least make some reinforcing plates to go under each mount. Based on the size of the foot pad, and available space underneath.
If you want to go next level, have custom anchors fabricated to bolt the cage to the frame. More work, but probably the best of the methods for a bolt-in cage.
Paul