Yep! You're not really moving the library anywhere, just organizing it and accessing it via Media Center. Other devices can access your files the same way they do now, through network shares or whatever.
For example, I have all of my music, images, movies, and TV shows all organized using MC running on my main PC. The files themselves are in a mix of places, but most are on a NAS device, and I have two NVIDIA Shield TVs (they run a version of android) that have Plex running on them for streaming content. One of the two is actually the Plex server.
As far as using labels or keywords instead of the shortcut-based structure you're using now, MC has some built-in tags that allow for creating a type of hierarchy like you mentioned. I think the primary ones are People, Places, and Events. Ordinarily you'd just assign a single value, but if you can use the \ character to nest them so you can set up any structure you like.
For instance:
Mary
Family\Mom
Friends\School\Doug
US\Wyoming\Yellowstone National Park
US\Parks\Yellowstone National Park
Birthdays\Mine\30
Christmas
etc.
And if these fields don't meet your needs, you can create new ones that will. You can set up any kind of hierarchy you like, then set up views that include these tags and have instant access to whichever category you want. You can easily search on them too!