No reason to tile the closet - you would normally install a water heater on a drip pan - a 20" to 30" round pan with a 1" drain fitting attached to it ( like these at Grainger :
The pan itself will catch the first two-three gallons of water and that will be enough for anything other than a major leak. As far as the water sensor shutoff, it may not be as useful on a water heater because by shutting the power off you can only eliminate one possible reason for the leak - heat expansion, and even then that would not go away quickly, the heater would have to cool down first. Your most damaging issues will have to do with water supply and other piping that the sensor can do nothing about.
Your best course of action would be to make sure the drain fitting is connected to a piece of PVC pipe that can actually drain somewhere reliably - outside is how it's normally done. Another possibility is to have it drained to a bathroom sink on the floor below and connect before the P-trap (the airlock that prevents sewer gas from entering the room through sink), similar to how washer machines and dishwashers drain.
That should cover you in 99% of water leaks related to a water heater. There's always a chance that the leakage or burst is so bad no 1" pipe can drain it quick enough. But then, there's always a chance that a storm will do damage or some other such calamity - that's what the homeowner's insurance is for.