If the energy you use for heat is generated by gas, it's more efficient to burn it directly, and the emissions produced from manufacturing all the new stoves likely out way the emissions produced over the stoves lifetime.
So, I'd say it's only helpful if you are getting a new stove anyway.
Of course, one also has to consider the leakage of methane that occurs with all the residential natural gas distribution, which is significant. Methane being 25x the greenhouse potential of CO2 means there's a lot of hidden environmental impact.
So, I'd say it's only helpful if you are getting a new stove anyway.