Repitiching Cider yeast for Ginger Ale.

[Firestix]

Any thoughts on repitching yeast (Nottingham) from hard cider into a batch of Ginger Ale (non-alcolic)? Is this a bad idea or simply a possibility for interesting flavors.
I'm also considering repitching the opposite direction Ginger-->Cider to add a slight hint of ginger flavor to hard cider

Thanks!