Yeah, a breaker box operates in any orientation.
"Should" you mount it on the floor?
The main considerations are that the box should be protected from damage (including that caused by dirt, dust, liquids, etc getting into it) and that it should be accessible. A place where the installation is practical is convenient, too -- it needs to go somewhere such that the wires can get into the box, and your hands and a screwdriver can get inside to make connections, etc.
If you meant for it to be oriented vertically, up against a wall, with the bottom edge touching the floor, sure that seems reasonable (though inconvenient to have to lay down to work in it). If you meant for it to be down with its back flat on the floor, I'd suggest looking for a better alternative.