Yes it will and does work. But, you are heating the circulating water all the time. Unless you have a need for instant hot water all the time, you will spend a lot more heating all the time, rather than just keeping the water in the tank hot. With a pump, you can save some by insulating the pipes. You can try it by putting a valve on the end of your kitchen faucet, then leaving both the how and cold valves on. Then both the hot and cold lines will contain cold water, and if you want cold, you have to run out the hot.
