I thought the question was going to be, does the stress of childcare shorten a broodys life? LOL
I mean, it is hard on them. 3 weeks of barely eating enough, then barely able to take baths without chicks sitting on their heads and scooching under their wings.
We recently let ours go broody this summer instead of fighting them all summer like last year. It's easier on us not having to raise chicks in the heat! Some hens go off laying in these temperatures anyway.
So there are many variables, you'd have to directly compare the same breed/bloodline, in the same environment and housing, on the same feed, and then let some go broody and raise chicks while others are never allowed (clearly marked hens). You'd have to test it at a big enough scale to get meaningful data.