It's impossible to win with converting a fossil fuel X into something and then to convert back to fossil fuel X, because of basic thermodynamics. If you want to convert fossil fuel X to something to convert to fossil fuel Y, you may be able to "win" over the current situation but you will very likely never get to get zero emissions in the system as a whole, because of the first step. It isn't necessarily impossible to burn X tons of CO2 and pull X+delta tons of CO2 out of the air, depending on the exact binding energies of the chemicals involved (which given that both are fuels, probably don't have an advantageous difference you can exploit), but you'll certainly be paying somewhere else to do it. And given that pulling CO2 out of the air at scale is quite challenging even on its own merits, it probably can't win in a practical manner.

If you're going to pull CO2 out of the air you pretty much have to be using a non-CO2-generating power source to do it if you want to net CO2 withdrawal.