I'm not sure about a URI, but I think for the most part, if the cats are in separate rooms, you'll be ok.

Although it is best to get it to a vet ASAP and have it checked for everything. Take a stool sample with you so they can test that also. It's quite common that strays are found to have worms or some sort of bacteria since they've been eating who knows what to survive.

Sounds like poor kitty has some issues that need to be cleared up before he/she is introduced to the rest of your clan. Good luck!