If you don't break the behavior and you're not going to have her incubate eggs, a broody hen could set much longer than the typical 21 day period and it could have detrimental affects on her overall health. They don't eat or drink much while they're incubating, but they don't need as much because they're not expending as much energy. But if they weren't setting on eggs that would hatch they might stay there indefinitely.
Although I did once have a hen whose first clutch of eggs didn't hatch, so I gave her a new batch of eggs to incubate. She was setting for 6 weeks straight, and is none the worse for wear today. Has anyone else had a hen set for longer than that?
I guess you could allow your hen to continue to set on whatever she's got there, fake eggs, golf balls, dust specks, and see if she eventually gets discouraged on her own. But if she seems to be growing weak or ill you should take her off immediately. You also need to keep checking under her for new eggs the other hens might be laying there. And I wouldn't leave sterile eggs under her, they'll go bad & pop.