Yes. The interior or my coop is OSB, so I definitely wanted it protected as well as stylish. I primed with a cover all primer and then applied a Tiffany blue exterior paint. You can hardly tell we used OSB and it should hold up for a long time. If you used plywood, your painting job should be even easier.
You will be very happy with a painted coop interior. Some creative people use wallpaper as well, but that could peel with moisture and time. I've never tried that, but it seems fun!
I will be sharing photos of my completed coop in a thread on BYC here shortly if you would like a peek.
In a moment, I'm headed out to Lowes to buy some paint for a cabinet hutch I found Free on the side of the road. I intended to hang it on the wall in my dining room for shelving, but it wasn't working out, so it's headed to the coop as a nesting box apartment.
I think I would only worry about paint toxicity for my birds if it was flaking from the wall and they decided to eat the flakes.