No you lose energy in the transfer.

While burning nat. gas is efficient, you do lose energy in the process.

A coal plant is 50% efficient, and CHP plant is 80-90% efficient.

A nat. gas heat pump is 80%-93% efficient depending on the money you want to spend.

A standard efficiency nat. gas furnace is at least 80% efficient, they top out at 98% efficiency.

Pretty obvious that converting from heat to electricity to heat is going to be less efficient than just converting to heat.

Not to mention the furnace is more efficient than the gas plant (max of 98% compared to a max of 90%).

Also the transmission and storage of nat. gas vs electricity is more efficient.