...is it possible to run them both on the same machine using the same library of books? In a perfect world, I'd be able to treat them almost as separate programs (buying a new copy of FGU while using my current copy of FGC), both drawing information from the same library. Thanks!
You can have both installed at the same time.
Make sure you either accept the default install locations, or if you customize them, make sure both FGC and FGU have separate application/data directories.
As long as your purchases are tied to your account, when you log into the app, it will pull your purchased items in both, that is assuming the product is compatible with both, most are, but there are some things that only work in FGU like the map packs.
Campaigns will be different.
DO NOT use the same data directory because once a campaign is opened in FGU it can not be opened in FGC.
I play in both FGC and FGU games and run FGU games,
I guess the only extra bit of clarification that I can add is that if you have any addons/extensions that _don't_ come from the Smiteworks store, you'll have to install (and update) them separately for FGC and FGU.