No, EVs are not obtained from the Day-Care/Nursery. They can only be obtained by KOing wild Pokémon, using Vitamins (HP Up, Protein, Carbos, etc.), or by using Super Training/Isle Evelup. The only purpose of the Day-Care is to breed and level up (unless it's Sun and Moon, in which Pokémon no longer level up in the Nursery.)