I don't really see why you couldn't do it. Main issue I can think of is getting a piece that big (need a really big kiln), and getting it fired without cracking/warping. About the glaze, I'm doubtful it would get rasped off, it's basically a thin layer of glass on the clay, if the rasping doesn't visibly scratch glass aqurium sides, I don't think it would have any affect on pottery glaze. But I think unglazed would probably look better, and be better for growing algae/moss.
You might have more luck going with making a bottom out of concrete and sealing it, or using the same method people use for backgrounds, and just stick it on the bottom of the tank.
I'm really fond of the stryofoam coated with an epoxy/sand mix, but I have no clue how that would hold up long term if something was constantly rasping on it. You may be able to even skip the styrofoam, and just go with a layer of epoxy/sand.
Do you want the entire bottom one piece, or are you willing do do tiles or a mosaic type approach (if you combine it with rocks/driftwood that stick up out of the tank, you could mask the seams fairly easily), and are you looking for a textured/scaped bottom, or just something plain that doesn't look like glass?
If you are willing to do tiles, I'd check out what's available in the local bigbox hardware store, I think they typically carry 18" square tiles, I've seen ceramic, slate, and terracotta (I use the slate to mount driftwood for my tanks).