I would have to say that you will not get a plant from these roots. I have dug up many daylilies and the roots have been cut and left behind just because I have no idea where they are when digging or these may be seedlings I'm getting rid of and don't care if they roots get cut or not. I would think if you could grow them from these roots then I would have more daylilies than I could handle. And I would think that more people (hybridizers) would be doing this to get more plants faster to introduce.
Now on the off chance that a piece of the crown is left attached to these pieces of roots then you get a 50/50 chance that a new plant will grow. It's not the root that produces a new plant, but the crown. That's why if you break a fan off and there is any piece of crown left on it it can grow more roots and grow into a new plant and new fans will grow from the crown where the fan was broken off from. Now a lot of times these broken fans and crowns will rot and die first, but I have seen this done time and time again and they regrow the roots; you just have to keep the crown or fan from staying way too moist and the insects from wanting to eat away at it. I usually spray them with a fungicide (Banrot) to ward off any fungus/bacteria and will drench the soil/crown/fan a few times over the next week or so. I will also include a systemic/soil insecticide to ward off any fungus gnat larvae and other wormy things from wanting to eat away at the exposed crown.
This is just IMHO and if I'm wrong so be it, but I just don't see it being the norm.
