Having had them in a shower I can answer yes to this question. You're standing on a hardwood floor, which most people like. Far easier on the body than tile surfaces.

Is this custom or are there off-the-shelf products available?

would the wood stain discolor the concrete beneath?

The teak floors will not stain or discolor the concrete beneath. At least the teak we use, has no stain added. We simply put a light coat of Teak Oil on the mats, which provide a really nice finish, but will wash away over time. It will not stain the concrete (however you will have to lift them up to do some general cleaning.