It's not a bad idea in principle. Hydrocarbons are the holy grail in energy density. Take CO2 and H2O, add in some energy and you've got yourself some hydrocarbons, and lovely breathable oxygen. Burn the hydrocarbons with some good old oxygen from the air, you've got yourself some CO2 (boo), some H2O, and energy to propel the plane. Here's the thing, if we still need to use hydrocarbons for things like planes, is there no easier way to off set it than making the fuel synthetically? Also, if the energy used to make the fuel isn't zero carbon, you're wasting your time, so until we have zero carbon energy, this idea can't work.