There is a belt fed .22 rifle advertised in the US. As mentionned, the feed system and its capacity isn't an issue with a rimfire. If its a new design, a FRT entry would have to be created to get the gun into the system. I would imagine that if there were a belt feed add on for a 10/22, let's say, the rifle would still be a 10/22. A variety of different sized feeding devices are already available for the 10/22, 5 to 50 rounds, doesn't seem to make any difference.
Designing and manufacturing a .22 belt feed system would certainly be an adventure, and getting the thing to work reliably would be a real challenge.