Yes. And if you use a stripper or something to remove the paint (and not the kind you find in a night-club, ) -- use care since some of them can do funky things to fiberglass.
I think paint stripper would be a waste of time and effort on a fiberglass door. You might want to lightly sand the surface, but even that might not be necessary, depending on the paint you use.
I agree with G.S. This is a straightforward paint issue....surface prep is the key. I wouldn't use any chemicals, not even liquid sandpaper. A little TSP would probably take any sheen off, then I would use a good coat of primer and best quality acrylic topcoat.
ive done them with auto paint, scuff them down, degrease and shoot the paint, you can have it mixed in any color and any amount of shine. use a single stage with a hardener and youre good to go. you can even wax them once a year.