Manning either doesn't use a mouth guard or never takes it in/out - he changes the plays multiple times, and I haven't noticed him taking a mouth guard in and out. Do you know which it is? I went to try to find some highlights but I couldn't tell if he was using them because the quality is somewhat low and doesn't show enough of the pre-snap stuff.
I would say the majority of pros don't wear one at all. Just my opinion/observations but I didn't research it or anything.