We had a rat problem not Christmas just gone but the one before.
Just a singular rat.
It was in our kitchen, but there are no possible entryways in through our kitchen directly to the outside. We don't open windows or doors and leave them open, we don't have food scraps laying around etc.
It took us almost 3 months, several different kids of traps, an expensive drain survey at £200/m, thousands in appliance repairs, a pretty penny in wireless nightvision portable cameras, and hundreds in getting specialists in to detect where the problem came from.
The conclusion was that as we are the house at the bottom of the hill that gets all the flooding, the drains had overflowed, rats evacuated the main drains, this rat had gotten up our drainpipe, up through the toilet, made its way into our airing cupboard on the landing which doesn't have a door, down the old boiler pipes in an old chimney flue, and out of a hole that was never filled when we were having the kitchen renovated years ago.
We don't know for certain of course, and it's possible the rat slid past us when we were letting the dog in or out but as the professionals said that's less likely because they're very wary of people and they're mostly nocturnal.
In the end we ended up catching the rat as it triggered a trap, startled itself, ran through a glue trap, skittled across the floor and got stuck in a humane trap. We did get pest control back out to dispose of it, but I did give it a nice final meal before we sent it off 😬 felt really guilty posting the contents of a lunchable through bit by bit but the advice we got was it was best to have it safely and humanely euthanised because they're smart little creatures that know how to find their way back to a good meal ground and warm home and they can get very pregnant very fast on their travels back.
So yes, in short, it seems like it is possible that rats can get up through your toilet but they'll only usually do so in an act of desperation because it's a lot of effort.