Does Janna's spells continue to cast when she uses Zhonya?

Just like Fiddle's ultimate, Morgana's ultimate,and Karthus' defile. Does Janna's ultimate still persist if she uses Zhonya? Also does her Q continue to charge then release if she uses Zhonyas? Sounds like a nifty combo. Just wondering her, ap scaling is pretty low so seeing an ap Janna is quite rare, and it does sound op to continue healing during team fights uninterrupted in the middle of all your front liners. Also sounds pretty strong to still be able to do damage and heal while in this state. Just wondering