A 6 inch diameter tube would have very low flow velocity in it, so the CO2 bubbles would just float to the top and stay there. You should try to get a high enough flow velocity in the tube to keep the bubbles suspended in the flow for a few seconds, for best efficiency.
I don't see a good reason not to put a heater or heaters in the CO2 reactor, except that if the CO2 bubble gets too big, it could cause the heater to get too hot and fail. The water is all that keeps the heater "cool". If I wanted to try this I would add a needle wheel type powerhead to recirculate the CO2 bubble, chopping it up into tiny bubbles. But, that gets you back to pumping some mist into the tank.
Maybe the 6 inch tube should be used for something else?