I helped install a system like that with my brother-in-law when he owned a laundry mat so the machines would have instant hot water. (this was many-many years ago). The principle is to put a return back to the water heater inlet from the end of the hot water line. The water is then in constant motion with a circulating pump.
Yes, you can do this, but you'll have to have a dedicated pump, either battery or AC. Most likely battery, like your on-board water pump. Then the water will constantly circulate, and your water heater will run a lot more. That's not so bad if your on electric, but if you're on propane, your water heater will eat that up much quicker.
So, you need to make a continuous loop between your hot water pipe at the sink and the inlet at the water heater, and install a circulating pump.
It can be done, but if your water heater is THAT close to your sink, why? Having that pump run 24x7 would drive me nuts!
