As long as it's large enough that it wont fall through the slats in the baskets, why not? The water level wont be so high that the perlite will wind up floating.

Just use expanded clay? It can be reused if you wash it down with a bleach/water combo after every few months or so after harvesting.

Or boiling hydroton will kill most of your problems bacteria.
But yeah, perlite should work.

"But yeah, perlite should work."

You sure about that?

"You sure about that?"

Why wouldn't it? Perlite is a well known hydroponic growing medium (same with vermiculite). They both will float, thus it wont work well in a flood and drain system. But in a water culture system (deep water or not), the baskets don't hanging down more than about 25% into the water at most, and in a lot of cases not at all. So unless the water level is set to high so too much of the basket is submerged, there's no problem of the perlite wanting to float.

Little tip: Put something over the medium to keep it from getting light. Otherwise it will get algae pretty fast. Perlite seems to be an algae magnet. You can cut a circle or square from a black plastic bag and put around the stem, for example. Perlite works, but if you didn't already have it on hand I would suggest not buying any. It's a little expensive and there are cheaper media that work perfectly.