No.
A queen is fed copious amounts of royal jelly so a nuc just doesn't have the nurse bee population to produce well-fed queens. A nuc is a good home for a queen cell but producing them really requires a full colony (or equivalent). Whichever race of bee you work with, you can't go wrong if you follow
Michael Palmers recommendations. I raise lots of queens and use a method very similar to this.
EDIT: If you had 2 colonies (as beginners are recommended to do) and one of the queens was quite old, pop her in a nuc with a frame of brood, a frame of food and a few frames of comb. Leave her colony for 9 days then go through it, shaking all the bees off the combs and destroying anything that even looks like a queen cell. They are likely to be unhappy about this so do it with care and consideration to what is going on around you. Make a space in the middle for a frame of grafts (this configuration will easily support 20-30 (but you don't have to put that many in if you don't need them). After 5-6 days, the cells will be sealed and you'll be able to make up mating nucs with your cells. You can leave them a few days but you'll have to cage them (i.e. Nicot cages) if you intend the virgins to emerge in this colony.