Is this something that might be possible? It sounds like it would be pretty useful.
No idea, and yes it would.
I have a couple of boxes sold under the Medion brand (Aldi) that connect to your home network by Ethernet or WiFi, and have three USB ports and an audio jack in them. You have to run a utility on the PC, but it finds the boxes on your network and any USB devices connected to them, and you can tick a box to selectively enable them on your PC and bingo - it's like they are plugged in locally. You can also transfer your sound output to the extender's output socket - which is great unless you are watching video, when the lag is intolerable.
Unfortunately I bought one when they were in store, found out what a brilliant device it is and scoured the Aldis local to me and Super Lurker and got another, but not been seen since. I guess they might come around again.