Shortly after we bought our house the 30A fuse for the cooker circuit blew, and I found that had been caused by mouse damage. There was quite an area of scorching, and I think we were lucky it didn't cause a fire. Surely an RCD would have reduced the damage and risk from that sort of issue, as there's a good chance it would have tripped before the damage was extensive enough to cause a full-blown short.
Not impossible but, I would say, pretty unlikely.
If the mouse damage resulted in and L-N short, then an RCD would never have noticed that. Even with an L-E short, it's not all that usual for a 'progressive' short to arise (i.e. one which starts off high impedance {but enough to trip an RCD} and then gradually reduces until it gets low enough to blow a fuse or trip an MCB) - with rodent attack, it's usually either 'all or nothing' (i.e. no short or low impedance short), in which case an RCD would not operate any sooner than would a fuse or MCB.
If the mouse exposed the bare L conductor and then peed onto that and the earth/CPC, then I suppose that might have caused an RCD (had there been one) to operate before a short arose!
Kind Regards, John