Sorry for the silly question but if the new queen can?t go for her maiden flight then will she be able to lay eggs?
If she cannot complete a series of mating flights, she will be able to lay eggs but she will be a drone layer.
It the queen cell is nearing time of hatching. I think I would try splitting the hive and moving the brood box with the active, mated, laying queen to a new location and leave the brood box with the queen cell and brood in the exact location the current hive is now. The brood box with the active queen will be able to continue on and recover its foraging bee force in it's new location.
The box with the queen cell that has not hatched yet will eventually hatch and conduct her mating flights. Once the field bees leave the brood box with the original active queen in the new location, they will return to the brood box in the original location bringing in much needed resources. You have an approx. 80% that the new queen will get fully mated and return to the hive. After about 3 weeks, I like to take a quick peek inside the hive with the new queen/cell and check for eggs or new capped brood.