No. Not to start a new colony. You can get away with very few bees to simply get your queen mated. But to actually start a colony and have the queen lay and build brood, 12 is not near enough. Nurse bees feed individual larva as many as 1200 times per day. 3000 times on the day prior to capping. They will also need to keep the queen constantly fed. And the brood warm.
The smaller the number of bees, the fewer eggs the colony can support and the slower the nucleus colony will grow into a sustainable size.
If you want to just experiment, I would probably start with no fewer than 500 and observe how large of a brood area they will keep tended. Also, I would leave sugar syrup on and rob frames of pollen from other hives to cut down on foraging needs.