
Some of the anode rod will dissolve in the water. However, the loss of anode metal is not usually symmetrical so rod material will may break off into the heater from road vibration, etc.
I have found that it is a good idea to flush out the water lines by removing the aerators from the faucet outlets, and flushing some water through the lines at the beginning and end of each season.
I also wash out the aerators, if I notice some whitish sediment in/on the aerators.
The amount of rod loss depends on the chemistry of the water used. I have had rods last multiple years and then barely last one season. A rod that is nearly dissolved away is demonstrating the protection it has given to your heater. Replacing a $15 rod is certainly cheaper than replacing a water heater tank.
Over the last couple of seasons, I have been draining the heater tank, if I do not expect to use the Pod for an extended period of time. The longer the time water sits in the tank, the more loss of rod material. I make sure that I fill the tank before I leave for the next trip...I don't want the tank to burn out because it was empty when I turn on the gas or the 110 house current