Rocket Stove Exhaust Gas as Greenhouse Warmer

Hi,

I'm in the theoretical stage of learning about permaculture and all its associated loveliness.
I watched some wonderful vids on rocket stoves, and want one.
Having thought about wanting one for a bit, I then thought about the permie concept of benefit stacking, or whatever it's called.
And I thought, surely we can use the exhaust gases - room temperature co2 and steam?
Surely a greenhouse is the ideal recipient of these gases.
Warmth.
CO2.
Moisture.

Has anyone run a rocket stove exhaust to their greenhouse, and if so, with what results?
If not, why not?
Thanks.

W.

There are other components of exhaust gas. Nitrogen compounds etc. People should not breath any gas whose constituents are unknown and highly variable.