Steam from RMH to increase humidity in greenhouse?

So I've been watching lots of videos on rocket mass heaters and noticed that quite a few people have them installed in their greenhouses which I think is really cool, and it got me thinking; Since the exhaust is mostly water vapor, why let it go to waste by sending it outside? Would it be feasible to maybe have some kind of valve that you can turn to either a) let the vapor out like you normally would or b) have the water vapor come back inside the greenhouse to increase humidity if you wanted to grow more tropical-type plants? I guess if the exhaust isn't 100% water vapor, then you might be letting a tiny bit of smoke back in, but that's probably no worse than having a conventional wood burning fireplace in your house, right? If you used a plastic pipe (like PVC) for the pipe that comes back into the greenhouse, you wouldn't have to worry about the water vapor condensing and rusting the pipe, either.

So what do you think? Does it sound possible, or am I missing something?

Danny Carm: I don't know if you ever saw the movie 'Apollo-13 ' the movie that made the line "Houston,- We have a problem! " a meme, and part of our culture and Language.
The gist of the story is, after an on-board explosion of equipment thought to be only of minor importance, the mission had to be aborted mid flight in an effort to save the crew,
a build up of carbon DI oxide nearly killed the crew, it was only due to clear communications a cross thousands of miles of space that a jury rig of the surviving equipment
was built, and proved effective in reducing (Absorbing) the CO2!

Plants produce oxygen while exposed to sunlight, during hours of darkness they are obligate users of O2 for cellular respiration, your plan to increase Water vapor can best be
served by the introduction of fowl- like chickens released to an understory of the green house where they will 1) warm the green house 2) release safe levels of CO2 and 3)add
water vapor ! not by introducing possibly dangerous levels of CO/CO2, remember, you only get to be wrong once ! For the good of the craft ! Big AL !

Ahh yes, that definitely throws a wrench in my plan. Oops.