Possibly, but you wouldn't know until you try, whether she would go the course of sitting for more than three weeks, as it would take up to another week to get the eggs you want unless you know a local supplier who has some ready for collection.
If you try this, you wold need to give her a broody coop and a small separate run, rather than leaving her in the nestbox where the others come. Also she should be freshly wormed and are fully checked for mites etc before she begins her sitting. Any chicks she hatches this year would probably not come into lay until next Spring as by the time the pullets were 5 months old it would be November and the days would be too dark to stimulate them into lay. This is OK if you are happy to let them grow on at their own pace.also, think hard now about what you are prepared to do with the unwanted cockerels you will hatch.