You'd have to remove the carpet, and weld that thing into place, directly onto the body to really stiffen the car. Most morons will simply screw it over the carpet. Then it's just more weight and a bother to back seat passengers.
it would help, but only if the center section is bolted onto the center tunnel. A "B" pillar bar (connects the center pillars between the pillars' height), however, would have a better effect in chassis stiffening, but of course you'll need to remove the plastic trims and it'll make a nice place to bolt on the shoulder belt from a 4-6point harness.
when the brakes locked, it really hurting the balls if you don't secure a 5/6point properly. Been there, done that..Ouch.