I just tried AP mid karma in blind pick. Naturally I don't know what I'm doing or how to build, but I think I managed to keep somewhat even, and the opposite AP mid wasn't very aggressive.
However, I don't feel like she can really work in that role right now. She doesn't do much damage without her ult, even if you stack AP + lich bane. I think the thing that bothers me even more than that is that trying to clear waves is really finicky. If you aim the Q slightly wrong, you have to wait another 4-6 seconds, and you'll probably miss some minions. I feel like most other mid champions, say Lux, have some way of hitting minion waves that doesn't explode on contact.