Does agapanthus re-grow from bits of root?

I took out an old and nothing-special agapanthus a few weeks ago. I got all of the woody crown and thick roots out, but there are lots of broken-off bits of brittle fleshy root left, a lot thinner than a pencil but thicker than cooked spaghetti. Will they grow? If not I won't waste time picking them out before I plant something else there.