Congrats on the new rig!!!
If/ when hooked to city water, yes, your wh will fill when you purge the air out of the line by turning a faucet on as long as the wh bypass valves are set correctly. BUT... even if using the fresh water tank, the bypass valves would still neeed to be in the correct orientation. The valve in the middle should be turned off, and the valves on the input and output of the wh should be turned on letting water into the wh. Reverse the valves when it/ if you need to winterize, making sure to drain the wh tank.
Make sure to fill the wh tank and purge of air before turning it on.