For electricity-to-heat conversion, heap pumps are indeed much more efficient relative to resistive heating, yes. About 4 times more efficient.
In absolute terms, though - that is still only 50% of "Carnot cycle" efficiency.
https://en.wikipedia.org/wiki/Coefficient_of_performance
Similarly, heat-to-electricity conversion is about 50% efficient in best case:
https://en.wikipedia.org/wiki/Thermal_efficiency
So, in your scenario (heat->electricity conversion, then transmission, then electricity->heat conversion), overall efficiency is going to be 50% * 50% = 25%, assuming no transmission losses and state-of-art conversion on both ends.
25% efficiency (a.k.a. 75% losses) is pretty generous budget to work with. I guess one can cover a small town or a city's district with heat pipes and come on top in terms of efficiency.