Uh, probably a bad idea.
It is not just air movement. Any combustion requires ventilation. You can do it two ways.
You could use a vented heater. In this case, the outside air is the source of oxygen for combustion and this outside air source is built into the heater.
You can use an unvented heater. In this context, "unvented" is a misnomer; the ventilation is not built into the heater. You still have to ventilate. You just do it with a hole in the wall or other deliberate or unintended infiltration.
In the case of the vented heater, the CO2 and water vapor from combustion largely or entirely go out through the ventilation process. You gain no CO2 or H2O advantage there.
In the case of the unvented heater, the CO2 and water vapor from combustion are dispersed through the greenhouse. Unfortunately, so are all of the other unwanted byproducts of combustion such as carbon monoxide and ethylene. You don't want carbon monoxide and ethylene.
In order for an unvented heater to be operated safely, you have to meet certain passive ventilation requirements. That is to say, you need a hole in the wall of a certain size, so many feet from the heater. In this case, as you might guess, you will loose much of the benefit you would gain from the CO2 and H20 combustion byproducts.
Unvented heaters are problematic enough that some states prohibit them.