Intuitively, that doesn't make any sense.
Initially, the water tank had no mineral deposits in it. It was factory new and perfectly clean, right?
So assume that over time, the water going through the tank deposited minerals in it. Then logically, the water coming out of my hot water tank actually had LESS minerals in it than straight cold tap water (because it had dropped some of its minerals in the hot water tank, whereas the cold water just came straight out of the tap).
So assuming that's the case, why would the water suddenly switch to PICKING UP the deposited minerals? Isn't that saying that my hot water is currently making my hot water tank CLEANER, by removing minerals? At what point will it switch back and start depositing minerals again? Is it some sort of cycle?
At any rate, given the thousands and thousands of gallons of water that go through that tank, I think any increase/decrease in mineral content would be absolutely trivial, and completely imperceptible in the final taste of any beer it is used to produce. And it saves me a solid 20 minutes of heating strike/mash water.