Nope, you want everything, in every file to be relative referenced files. It should have no drive letters or anything.
Then, any ‘copies’ are just the folder structure. You define a top level folder and EVERYTHING is under that, and it’s that which is copied (likely with something such as Syncthing) to to remote PC’s.
That way it doesn’t matter what drive or even what other folder names precede it, any linking should still work, since the folder structure that the production uses is still the same.
As for Kitsu, I messed around a bit with that myself from a local setup point of view (Using Kitsu for solo production tracking if you want some reading while trying to fall asleep).
My advice, don’t do it. Largely not worth it for just 2-3 people. A Google docs spreadsheet or much the same thing should be fine.
What will be important is folder/file structure and being a drill sergeant about everyone following it.
I made a couple of videos to get you starting to think about some of that (https://www.youtube.com/watch?v=4dgB-6K6_UE&pp=0gcJCYUJAYcqIYzv and https://www.youtube.com/watch?v=NCnmDKewrxc).