Should work fine, but using a raspberry pi for this is kind of overkill, but hey, it is up to you.
There's a high probability that an RPi would cause enough of a delay to get annoying after a while.
Might be OK for a proof of concept, but by the time you've mucked around with the RPi you might as well have prototyped it on an Arduino.
I had a go with this with a spare pi2 (which is now hooked up to my 3d printer) and a USB > null modem cable. It works really well actually, no latency that I could perceive compared to using a real serial mouse.
I could never get it working with the pi's built-in UART though, which was rather disappointing, it seemed to be the RTS pin wasn't working.