I used to raise queen cells by the the thousands, and it is a very complicated process. I have always wondered what the minimum size is required to get a couple of decent queen cells. It is quite probable that you can do it with nucs.
Basically, a strong four frame nuc should be able to raise a decent queen for itself if there are enough nurses, honey and pollen. But using it as a cell builder, is a different matter. It might work fine for a half a dozen good cells.
A very strong one story queenless hive can start and finish 45 cells. I used to use two deeps. The first would be empty. On top of this a queen excluder to prevent any stray queens from getting in or out of the unit.
The second story is where the action is. Here you would have brood, pollen, honey, and an inboard feeder if necessary to keep the colony pumped up. Fresh nurse bees would be added twice a week.