Yeah, you can paint the plate chokes, masked or not.
The varnish on the outside of the frame doesn't have to be there, we will sometimes brush it off carefully with a wire brush before painting.
Soaking the plate choke in any kind of solvent will remove the varnish that we do want to be there, so I wouldn't recommend that.
The best results I've gotten were from taping off everything but the channel frame, then spray painting.
-PB