Whenever there's a male and a female together there's a chance of fertility. How good a chance, well that's different. If you collected eggs before you saw them breeding, did you ever check one for fertility? It's possible that they've bred many times when you haven't seen it.
Typically the hen will either stop laying when she goes broody, or only lay one more day. The eggs ideally all hatch on the same day, so hens don't usually lay any more after the brood starts, as that would produce a staggered hatch.
If you want her to brood her own eggs, and you have some that you've collected to place under her, you can let her try to hatch them. If they're not showing veining at the right time then you can break her brood before she sets the entire month or more. If you have some eggs that have only been in the refrigerator for a few days you can try them under her also. Theoretically eggs for hatching should not be refrigerated, but people post about hatching refrigerated fertile eggs they bought from the store that were marketed for eating, so clearly refrigeration doesn't kill all embryos.
Alternatively, you can try to break her brood now, and start collecting her eggs when she restarts laying to store properly for her next brood. However, there is always the risk that she won't restart for a long time. The eggs are best stored at cool room temp (~50-55 degrees) for up to 7 days for best hatching, but some will still hatch with up to 14 days of storage, although the fresher the better. They should be stored in an egg carton, pointy end down, and tilted about 30-45 degrees, alternating right and left, 2-4 times daily. I personally try to store for no more than 10 days (unless I'm desperate for chicks from a particular hen, then I'll go up to 14 days), and as the "expiration date" appears I send the egg to the refrigerator for eating. Wash your hands before handling eggs for hatching to avoid contaminating the surface. Eggs should not be washed, just brushed off lightly to preserve the bloom, which protects the eggs from germs getting through the shell. Eggs that are severely soiled should not be saved for hatching, if possible. First time broodies should not be given too many eggs (6-8 is the maximum number I've seen recommended), as they don't have the experience to consistently turn and properly cover 12-18 eggs, so many eggs will get poor care at sometime during the incubation, resulting in poor hatch rates. Best to give a new hen a manageable number to learn on.
You can also save eggs, once she starts laying again, to put in an incubator.