I don't see you having an issue, other then if any light from the veg box can get back to the flower box.

Vegging plants don't really need much extra CO2 either. I doubt it'll hurt. Just not really needed.

Remember your Dry ice? The smoke IS CO2, and thus weighs more then air. Therefore it drops. CO2 from a tank is the same. It'll collect on the floor if nothing pushes it back up into the room.

SO,.. Keep in mind, if your line (hose) to the veg box comes out of the flower box at the bottom. Your veg plants might get more CO2 then the flowering plants. Same the other way too. If the line out of the VEG going back to the flower box is coming out of the bottom of the box it'll move more CO2 back to the flower box.

Should be interesting to see if it works out.

Oh and by having both boxes connected. You risk cross contamination should you ever get bugs. So be extra careful about that too.