Pizza stone as floor pizza oven vs firebrick
Short answer: No.

Long answer: this could probably be made to work, but only for a short time.  At some point, and probably within a few uses, the rapid heat cycling from the fire would cause the pizza stone to crack.

Pizza stones are made from corderite or clay, sometimes with grog.  This offers a smoother surface than firebrick, but that smooth surface is because of a higher amount of vitrification and less airspace in the ceramic.  This means they are less resistant to cracking due thermal shock, and the fact that your pizza stone is 1/4 a thick as firebrick makes that worse.

In contrast, firebrick is a standard 2.5" thick, and made from higher-temperature materials with more airspace in the clay itself.  These properties give it both higher thermal insulation, and higher thermal mass (so that it cools down slower).  Both of these properties help it resist cracking.