Not a good idea. Unless it has only produced a single, small, round bulb, each clove would form a new plant and you'd get a cluster of tiny cloves.
Better to dig it up and replant in rich soil, spacing the cloves about 6-8" apart. That way you'd get many big bulbs with large cloves. Try the allium forum for more details.

Your garlic will not go bad. I left some missed cloves in for several years, and when I finally dug them up, they were good size garlics. They would have been bigger, and more of them, if I'd dug each year and separated them, but they were fine.