I think the broody will sit until she sees some results....at least mine have. I make them carry on with the broodiness for at least a week until I know they are serious before I let them have eggs to set. Then I load them up with the eggs from the breeds I want and mark it on the calendar.
My second broody (sitting now) started broodiness for a couple of weeks and kept commandeering nests in the coop....I finally gave in and let her set a clutch. She is doing better than the last broody and is now sitting on 9 large eggs. She will hatch them on or around the 21st. The last time I did it this way, the hen actually hatched a couple days past the expected hatch date.
You have nothing to lose by experimenting with letting her brood a clutch and see how she does. Good luck!
P.S. I just put another determined broody on a batch of 6 last night and will let her round it out with her own eggs, as she is a Black Aussie. So far, she has been broody for a week and a half, but allowed to set for 2 days now....she is doing well and staying on the nest.