I wouldn't be the least bit worried about brining in the fridge, though I usually do it in the cave, or sometimes at room temperature if the fridge is full.
I am a bit concerned about the length of brining - how big was this Caerphilly? 24 hours is a long time in the brine. Yes, Caerphilly is normally on the salty side, but for the 4-gallon makes that I do, this would be too long.
As for additions - sure, you can add flavors to the Caerphilly. I will sometimes coat a Caerphilly with olive oil and smoked paprika. The flavor doesn't really permeate the paste, but as long as you slice it so that you get some of the rind, the smoky taste comes through in a lovely way.