It depends on the hen and the circumstances to a greater, or lesser extent. I've not let a hen sit for long enough to find out what, or if there is a time limit. I've had hens sit for four weeks and then intervened.Thank you all of you for your replies. We don't have any fertilised eggs, and I'm not bothered if she doesn't lay for a while. I'm undecided whether to try and 'break' her broodiness, using all your tips above, or to just go with the flow and let it happen. What would happen if we just let her get on with it? Do they just give up after a while? I cannot find any info online about what happens if you just allow a hen with no/unfertilised eggs to just get on with her broodiness.
I've very rarely had to do more than remove the eggs. The wire cage method is a last resort solution imo. Once the eggs are gone the hen may sit on an empty nest for a day and then spend the next couple of days wandering around puffed up and clucking. This year so far I've had 16 incidents of broodiness, one hatching and not had to resort to isolation once.

I wouldn't let a hen sit on unfertile eggs full stop.