Sure. They only spread by seed, so if they aren't allowed to flower and make the seed balls, they won't multiply. Fertilizing will definitely make lusher, fuller plants with better greens. I'd suggest a late summer/early fall application, and another very very early in the spring when they first start to show signs of life.

Also, if you REALLY like them, you might want to invest in a package of seed of one of the improved French or Italian varieties. I bought a package of Italian ones off the Thompson and Morgan seed rack a few years back at a local garden center, and there is a tremendous difference in size and leaf quality versus the wild ones. Of course, I also have found that the local rabbits recognize this, as they eat these and don't seem to touch the wild ones growing as weeds 15 feet away.

The link below is one I found for the same kind I have, "Tarassacco' I've ordered from this company before with good success, they have some neat things.

By the way, these are true dandelions (the perennial with yellow flowers) NOT 'Italian Dandelion' the more common vegetable, which is a actually a chicory (biennial, blue flowers).

Here is a link that might be useful: Cultivated Italian Dandelion at Gourmet Seeds International

Dandelion greens is a spring tonic and tasty green. Especially in spring time when dandelion leaves are young less bitter. Italian and Amish people has been eating dandelion greens for years. I read somewhere said it help purify blood and detox liver. It also very nutrious.