Yes. Even if they were fertile you can still use them as long as you collect them every day. Since yours are not fertile you could go longer but I'd stick to the every day collection.
Yes, people do that all the time. A committed broody hen will hatch turkey, pheasant, or duck eggs and will try to hatch door knobs or golf balls. It doesn't need to be her own eggs.
If you want her to hatch eggs I'd mark a couple of real eggs or get a couple of fake eggs and leave them under her while you get the fertile eggs. You have two basic approaches on how to go about hatching.
Some people isolate the broody from the rest of the flock. You can either prepare a pen with a nest, food, and water and lock her in there until the eggs hatch. As NatJ said the biggest risk is that she may break from being broody when you move her. Or maybe you can build a pen around her nest with food and water but totally lock her in and the other hens out for the duration. You will need to feed and water her and clean out poop.
If you let her hatch with the flock you need to mark the eggs you want her to hatch and every day after the others have laid remove any eggs that don't belong.
There are some variations of those but those are the two basic ways. If you decide on one let us know what your facilities look like and we can work on details with you.