So I'm a paranoid person, if they don't already have the parts for the replacement I would question how long they would take to acquire after turning the water off... Because while the hot water tank in theory shouldn't drain anything, if others start trying to wash hands, clean dishes or take a shower the water from the tank would still come out and then you are heating lower amounts of water and air in the tank.
So the what could go wrong always has me cut the breaker to the hot water heater before I shut off the water main.