Yes, that is correct. So the only way to improve on it would be get more work from it. Same power (watts) doing more work.
An example I think of this would be using a stirling engine to power a fan to move the heated air. It take 1,500 watts of power to make 1,500 watts of heat still. But if you sit a stirling engine on top of that heater in the room to be heated, then there are no losses or power used to move that air. All heat stays in the room. The tempature difference between the heater and air is what runs the engine to turn the fan.
Take it a step farther and you have 1,500 watts of LIGHT which equals 1,500 watts of heat, and a fan moving the heated air. Still only 1,500 watts of power for heat, but you now have Light and fans in use for free.
1,500 watts of electric heat is going to take 1,500 watts of power, BUT how much work will that 1,500 watts of heat do? If the heat is made and used in the same room, then any loses just go back into heating the room which is what you first wanted to do anyway, so therfore there really is no loss.
Not too serious here, but this IS ONE way to get more heat for less power
Use 1,500 watts of electric to boil water, run a small model steam engine on that boiled water, connect a small generator to that steam engine to make some power.
OK, there is NO loss in the engine or generator because any loss is heat and you want that heat to begin with. So all heat stays in the room, therefor there are no losses.
Any work done by the steam engine then is free work, so if it makes 200watts of power on 1,500watts of electric heat, then you actually only consumed 1,300 watts of power for 1,500 watts of heat.
So use the power grids 1,500watts to boil water and get 1,500watts of heat into your room while running the steam engine and producing 200watts of power which you also use for heating. You now got 17,000 watts of heat for only 1,500 watts of grid power.
That would and does work that way, how much power you could generate from a steam engine with 1,500 watts of electrically heated water I don't know, could be more or less. But since all you wanted in the first place is the heat anyway you got it and anything extra is free.
I like working model steam engines and have given this alot of thought since I am building one myself. How to fire the boiler and keep everything safe? Electric boiler should be as easy to control and safe as your hot water tank, just a bit different.
And as always, all heat stays in the room. Well at least as much as any other heat source would keep heat in the room.