You do need an expansion tank. It should go in the cold water line between the cold water shutoff and the tank inlet. It provides an air cushion. Each tankful of water will expand a little when heated and can trip the temperature/pressure relief valve if there is no expansion tank.
(The expansion tank will work anywhere provided there is no closed valve between it and the water heater but the inspector likes to see it quickly when he looks at the water heater.)
I have not read about drip tees in flues but I have heard about water vapor condensing in the flue and running back down into the furnace or water heater.
(One morning on WRKO Radio) The tub's not clean! Let's remodel the bathroom.
(One afternoon on WRKO Radio) It's time for an oil change. I'm going to trade in the car for next year's model.