I don't think so. We're talking milligrams in fairly large volumes of water contaminated with all sorts of additional compounds. To make matters worse, Pt and Pd may be both present alongside each other and they'll probably be quite difficult to separate to begin with.
Provided you could actually separate out the noble metals, you'd still have to convert them to usable salts to be able to reuse them, and the chemistry involved is typically not something you'd want to do around the house.