Sure; it's not an unreasonable approach for making such travel carbon neutral; the idea being you're sequestering parity amounts of carbon via the atmospheric gases -> fuel process, and nuclear power covers the inefficiency of such a process.

Downsides include:

1. It's only neutral. It doesn't remove gases we've already released.

2. The process is almost certainly extremely expensive. Until something like emissions taxes are levied, it will not be a competitive fuel.

It's slightly better than neutral. Captured atmospheric carbon would be stored out of the atmosphere in fuel tanks until use. And we could decide to capture and sequester more than we plan to burn again, since in this scenario we have the capturing tech sorted out.

Sure, under the assumption it's cheap to sequester more than all of the oil we extract out of the ground and consume today, then some could be stored to make it neutral or even positive. There are two big steps in there that might or might not ever happen.