Not as far as I'm concerned.  Before a hen even starts to lay she adds additional fat.  This extra fat is what she mostly lives off of while broody.  That way she can stay on the nest and take care of the eggs instead of needing to look for food.  Unless they stay broody for a very long time being broody does not hurt them.  As far as taking a break from laying helping them, they take care of that when they molt.  The numbers and size of eggs is to a certain extent related to what they eat.  I don't see the going broody being detrimental to their health as long as things are "normal" but I also don't see it being beneficial.
Not with all of them as far as I'm concerned.  A good rooster might perform certain duties (find them food, keep peace in the flock, break up fights, help take care of chicks, show them where to nest, or provide some protection or look out for danger) but not all roosters are good.  Most mature roosters are good when mating a hen.  Most does not mean all.  Some roosters are brutes toward their hens, not just in mating.  Often a dominant hen will assume some of these responsibilities if there is no dominant rooster in the flock.  I don't see a rooster always benefiting the hens and can be a detriment.  There are a lot of flocks out there with no roosters at all and the hens are quite content.  Some people may not be happy without a rooster in their flock, I like one myself, but I'm trying to look from the hen's perspective, not mine.  I believe that was your question.
I do not believe the presence of a rooster causes or enhances broodiness.  The absence of a rooster does not prevent broodiness.  Inheritance has a big effect on whether a hen will go broody or not.  Allowing eggs to pile up will not cause a hen to go broody, I've tried a few times and it never did work.  Allowing the eggs to pile up may encourage one, not sure about that, but they will certainly go broody without them piling up.