Not directly via the global color selector as far as I’m aware, at least not without some sort of scripting, which I can’t help you with. However, you can save a simple color texture with a brush that should load with it and paint in that color as long as the MRGB or RGB channels are active.
Remember that custom brushes will not load with a custom interface until manually loaded into the session, unless they are added to the startup items, which is something you should do sparingly. You should rely on Lightbox for more situational items that you aren’t going to be using every session.
Whenever I’m working on a project with a deliberate palette, I just save a “palette” object painted with all the colors I want to use, and I can sample freely from that at any time.