Using 6 gallon hot water tank as recirculation device
Let's say we're dealing with 70 gallons of water, and we're adding heat just by running a circulation pump to stir the water around. And, let's say the pump is a standard hydronic circulation pump of 100 watts (they actually seem to be a bit less). And, let's say that all of that 100W goes into moving the water about, which then decays into 100W of heat through friction.

100W is the same as 340 BTU/hour, where one BTU heats a pound of water by 1 degree F (love them Imperial units!). 70 gallons is 580 pounds of water, so we'll be raising the temperature of our water by 1.7°F per hour. If we start with 60°F water, and want 120°F water, then we'll want to end up with 60°F of temperature rise, which will take about 36 hours. But, we guessed high a few times in our calculations, so I'll estimate it would take closer to 100 hours to get up to temperature.

But, that's with no heat loss whatsoever. To avoid losing significant amounts of your precious heat, you'll have to insulate it all so that when the water is at 120°F the temperature falls less than a degree per hour. That isn't easy for a single tank; add in pipes and it becomes really hard.

After all that, here is my answer to your question: no.