Depends on how you want to look at it. Let's suppose your primary heat is gas. You are first going to put 3000 BTU's into the heating space and then use about 1000 BTU's of electric to move it into the heater. That's 4000 BTU's of energy when you could of directly heated the water with the gas using only 3000... In the winter time you will never beat the cost or efficiency of directly using the same fuel source as your primary heat to heat your hot water.
On the other hand since the cost per BTU for natural gas, coal or wood is really low this will be cheaper than regular electric heater since the cost per BTU for electric is so high. There is always an efficiency loss strictly looking at the BTU's though.
In the summer since the cooling effect and de-humidification are desirable if you wanted to factor in the energy savings for less energy AC/Dehumidifier the efficiency goes off the charts over just the normal efficiency.
This is not completely correct but I see where you're coming from. If you want to heat with a gas hot water heater, it's going to be vented and not 100% efficient. When you heat your house with gas and use a heat pump water heater, and if you need 3000 BTU to heat a certain quantity of water to a certain temperature, you will use the heat from the room at the coefficient of performance + heat generated in the compressor cycle = 3000 BTU, no energy is created or lost in the process, it either goes into the water or back into the room, which goes into the water, 100% of the energy used and moved stays in the house, nearly completely contained in the water. In your example, which was COP 2:1, 1000 BTU of electric heat ending up being used would only scavenge 2000 BTU from the home to do the same work of 3000 BTU of heated water... When you compare it to a vented appliance, you lose some % of the energy needed to the exterior of the building, whatever the efficiency of that appliance is rated, and you will always lose at least some energy to the vent. So in the vented appliance, you use 3000 BTU + losses in the water heating process.
You could make the case that using the primary gas heat in the water heater directly is more efficient in the total circuit than the ventless heat pump if the gas hot water heater it would be replacing is > efficiency of your gas air space heater. This is not really the fault of the heat pump though, just that you lost energy before it got to the hot water heater stage of the overall efficiency gradient. If you have a boiler that does both DHW and heats the home, a heat pump tank really wouldn't ever make sense to operate in the winter there - you'd just be trading part of the boiler's output for the fraction of electric that heats the water.
The BIG factor that needs considering in any winter efficiency margin comparison is that the house is a variable, lossy medium - you would need to take into account the fraction of heat that is lost from the initial air heating before it makes it to the heat pump as well. So an example would be a 98% furnace feeding a 4:1 COP HPWH, and say it takes 1 hour to put the 3000 BTU of final energy in the water, 600 BTU from the electric and 2400 BTU from the heated room. But, say you lost 30% of your initial heat from the furnace to the outdoors over that 1 hour period, so the 2400 BTU from the room was
not 98% efficient gas heat, but rather .98 * .70 = 68.6% efficient gas heat by the time it is entering the water heater gradient... Our example here compares poorly then to a normal non condensing gas storage water heater which would be about 80%, and the fancier condensing models are close to what a condensing furnace can do, at ~95%.
Cost is a different and separate factor on top of it all, and if the electric cost of running the compressor + extra room air efficiency losses is > cost of the direct heat losses on the replaced vented appliance, then you lose money in the difference during operation.
The summer is definitely a better use case overall for most users, the cooling+de-humidification is usually a benefit, removing unwanted excess energy from the home and discharging it underground into the septic tank or sewer system in the long run, like an open loop ground source heat pump in "cooling mode"