Green crust around water heater exit pipe
There is no need to drain the tank.  You will probably get some small amount of water on the floor but the tank will not run onto the floor.  Make sure that the main water supply valve is shut off.  The Shark Bite supply is a good idea.  Get one with the valve build in.  Just turn the control gas valve into the vacation mode while working on the water supply.  Then back on again when done.