Depending on the building’s construction and insulation, the HVAC system’s design, etc., no, the heat may NOT diffuse around the dwelling well. Haven’t you ever been in a house where certain rooms are perpetually much colder than others, even though they’re heated by the same furnace?
This isn’t relevant to the laws of conservation of energy.
Also, a lot of northern homes don’t really have a “furnace room” in the sense that it’s a small closet just for the furnace and water heater where heat might build up. Instead it’s in an unfinished area of the basement. It’s not technically living space, but some heat is desirable here so the pipes don’t freeze and your tools don’t rust and the floor above in the living space isn’t freezing cold and you don’t freeze either when you go down to do laundry.
At least here too natural gas is cheap because it’s basically a waste product from North Dakota oil fracking.
It is however relevant to the economics of a heat pump water heater. If the building’s design or whatnot does not allow all of the heat produced by the furnace to be used in a desirable manner, then “stealing” some of that heat energy to heat water is not inherently wasteful, and may in fact be a net positive.
For example, I once lived in a rental house where if you wanted the north bedroom to be 65 in winter, that meant having the kitchen close to 80 degrees. Nobody wanted the kitchen that warm, and the energy used to keep it that warm was essentially wasted, but it was a necessary side effect. A hybrid water heater able to scavenge some of that kitchen heat would basically be heating water for free.