You guys need to do a little math here - don't calculate the force of an impact ripping off the wheel well. Calculate the force of an impact that wants to flex the CHAIR, then the total weight of chair and occupant, then multiply by the length(s) of the mounting leg(s). A plastic chair holding a doll could probably survive the disintegration of the front of the bus. A 300lb guy belted into a single-post captain's chair like off a boat might tear out the bolts through 16ga sheet steel just from a hard stop.
The object in the chair wants to stay in motion, and the force of decelerating it will be transmitted up (yes, basically "pulling back" on the chair to slow it down) through the mounting leg(s) via the mounting points. That basically makes the leg(s) a lever, which multiplies the force applied to the floor. Also, remember that the force involved here is torsion, not shear. Sheet metal is weakest in torsion.
There's a summary of the math involved here, you can just adjust the numbers to suit:
There's a cute reference to unbelted occupants and windshields, which has nothing to do with this chair mounting case - but it IS a good reminder of what force-multipliers can do. A chair leg is a force multiplier.
An adult occupant sitting atop a 2' leg (lever) will have their weight multiplied by that distance in terms of the force they apply to those bolts. Add in a 2g+ hard stop (not even a collision) and now you have several hundred pounds of force involved. Now imagine hitting a tree even at 30mph - even at 10mph from a parking break not set! - and you could be talking several tons of force. Four bolts through 16ga sheet metal - that chair's occupant is going to be a missile. Sixteen bolts - they'll probably make it.
But now, put a 1/4" backing plate under there. This does more than just provide thicker material to bolt to. It's also going to help transmit more of that torsional force laterally, converting it to a shear force. To tear out the wheel well, the force is going to need to "rip" a much longer line of it, and it'll be doing it much further away from the mounting point. Where this happens, the force is now pulling mostly sideways, and sheet metal is much stronger in this direction. (You can prove this to yourself. Rip a sheet of aluminum foil in half the usual way - easy. Try pulling it apart sideways and it's much harder to do.)
Even without doing the math further (no idea what chair you're installing), the 1/4" backing plate sounds like a great idea here.