Jeremy,
That's a good question. The dichromate can stain things pretty easily, but I haven't tried it on anything glazed. It can leave yellow stains on fiberglass trays and other plastics, depending on the material.
My guess is that if you can avoid getting stains on things from the palladium solution in pt/pd than I think you will probably be fine with gum bichromate. Don't leave any cloudy water sitting around, though, as it may leave a ring on things that will build up into a noticeable stain over time.
I think the pigment is the majority of the staining that I see, but it wouldn't penetrate into a glazed fixture, so you souldn't have to worry about that.
---Michael