Rats CAN bite, yes. But for an average rat it wouldn't be without good reason. The only time a rat has bitten one of us with actual intent was when Reiji was overly hormonal and was still very angry from a fight. So usually only when something is wrong. A serious bite can bleed a lot, I believe Naz still has a small scar from that.
Link and Cid don't bite, but if you tickle them too hard they play back with their teeth, and they often give things exploratory nips, including body parts.