I'll admit that is a question I would never have thought of. I like questions like that. They make you think. I've never removed a rooster like that, so I cannot speak from experience, just kind of reason it out.
It is always possible that a broody hen will leave her eggs whether you remove the rooster or not. They are living animals and anything can happen. It just depends on how strong their broody instinct is.
If you remove the rooster, or any hen for that matter, from a flock, the pecking order will change. Assuming you only have one rooster, one hen will work her way into the flock dominance role. Depending on the personalities of your chickens, there may be a lot of fighting or there might not be much while this gets sorted out. In either case, a broody should not be involved in this. She has other things on her mind and she has such a bad attitude, the others don't want to mess with her anyway. I seriously doubt removing a rooster while a hen is broody will cause a broody to leave her eggs.