How much time for that? How big can that scale?
To give an idea of the current trend, every single day, near 100 million barrels of oil are produced. Each of those barrels make between 500 and 750kg of CO2 equivalent (source https://carnegieendowment.org/2016/02/09/breaking-down-barre...)
And that only counts as fossil carbon from oil (gas and coal should be added), that has been going for decades (at a slower rate, in 1998 it was 73 million of barrels/day, still a big number). And positive feedback loops are adding new carbon to the party as coming from permafrost thawing and other sources in increasing volumes, as the planet warms up.
So for making the trick carbon capture should not only offset what is being produced in that moment, but capture everything ever emitted till reaching an amount below the one we had in preindustrial times. And keep it that way for enough time to undo the warming and try to shutdown the bad feedback loops.
Creating synthetic fuel from captured carbon doesn't lower the amount of carbon in the system (once it is burned as fuel, at least), but if it is used instead of pumping out fossil fuels, at least will accelerate less the amount of carbon we still add to the atmosphere.
Having a small scale demo doesn't mean that it will be ever feasible a production of the size and the speed that will be needed.