I would hesitate to pour water into a clay or ceramic cooker--it could easily crack from thermal shock, and also it will be wet from the inside out & unfit for heating until thoroughly dried out again.
While I to would be very cautious about getting the inside of a hot Egg really wet, I have spilled a drip pan that was about half water and half grease. It was the grease that caused the problem. Immediate fire, and then several hours of baking to reduce the stain.
I have spritzed a pizza stone several times before baking bread without any problem.
I forget to what "cone" the Egg is fired, but I vaguely recall it was something like 2400 F. So, that is some hard ceramic.