First, I don't believe chickens can count. They have no idea how many days have passed since they started brooding.
That said, I do believe broodiness is hormonally controlled, and those hormones take time to develop and reach peak levels. Once a hen goes broody, her system starts on a 3 week cycle where different hormones flow and ebb. Trying to shorten that cycle usually fails as the hormones just don't support the next step in the process, mothering live chicks vs setting on a nest.
If the hen in question has a good history of maternal behavior, has raised chicks before and done well, you could give it a try. I'd be available to keep a close eye on things, though, as she may not accept them. If she's a new or untried broody, I'd go ahead and brood the chicks yourself and set more eggs under the hen.
I just had two broodies in the same pen. I let them set on air for the 21 days as I'd just set shipped eggs in the incubator. The night before my eggs hatched, a third hen went totally and whole-heartedly broody. Some of the chicks were near the new broody when I was grafting them to the old broodies, and she gave them some pretty good pecks and was very unhappy with their presence.