As many have mentioned already, such an air-to-petrol might be viable in the middle of the Sahara where sunshine is plenty and access is poor. Anywhere where plants grow well, and can be dried, there a more efficient way...
(1) Grow plants to create biomass
(2) Let the biomass dry
(3) Put the biomass into a sealed container
(4) Add heat to evaporate the biomass
(5) Pump the air out of the container through a condensor
What you end up with is a mix of hydrocarbon oils that can be refined into petrol and many other things. The collection of the CO2 is done for you by vegitation in the sun. You can use waste biomass (stems and leaves) from a crop that actually produces something useful besides biomass.
Here is another idea... the UK is experimenting with storing energy as liquified air (1), which can be heated later to propel turbines just like steam. One of the byproducts of freezing air (at 77K or lower) is solid CO2 which freezes at 174K. The dry ice is a concentrated source of CO2 that can be liquified at pressures above 5 atmospheres and chemically combined with hydrogen to produce hydrocarbon oils.
Of course, such a system would require more energy input than it would produce, but this is about energy storage and the production of clean hydrocarbon oils rather than energy efficiency. There are a few locales that will be able to produce more clean energy than needed and might have difficulty selling/exporting it -- such places might eventually be able to produce their own hydrocarbon fuels for more self sufficiency.