This is an often considered idea by those who are unfamiliar with the whole idea - but it is rather problematic on several fronts. If one practices good bio-security, the whole idea flies in the face of that. If done properly you would be looking at months - 30 days quarantine at the outset, then the time involved in integration of a new bird (days to weeks), then the time involved in the bird being in the flock to get to the point of likely fertility of eggs being laid then quarantine on the end side before reintegration back into the original flock for whichever bird (hen or rooster) that was moved to a new flock. All of this is on top of, if one's goal is to have the hen hatch the eggs, having to have the hen go broody during this time - otherwise she will have zero interest in hatching the eggs, fertile or not.
Easier is to simply source some fertile hatching eggs from someone who already has a flock that is producing fertile eggs and putting them under a broody hen.
