For a super efficient car your math seems about right. A gallon (~4L) of gasoline is roughly 33kW/h of energy, so 100-120 miles per gallon equivalent car is possible, but difficult (sorry for US units, that's how we measure car efficiency).

It may be good as a supplement like you said, or can possibly keep the AC running or something like that.

The problem is that moving a big thing fast and for long distances is energy intensive. So solar power is just not enough if you are expecting it to be self contained on a personal vehicle.

More to your point though, photosynthesis is an energy capture mechanism. In order to derive mechanical energy from the molecules produced (sugar and oxygen) the car would then need to react the sugar with oxygen. So in effect, you'd just be making a bad solar panel with extra steps.

So they are making an electric car less efficient by putting an energy draining device on the front? Fun concept but the thermodynamics don't work in their favor. It would be more energy efficient to just plug the carbon capture device into your house and skip the charging step.

I could be wrong, but I think there are also changes required at the consumption end to accommodate the change in gas. Same reasons why a propane boiler and natural gas boiler are not interchangeable without modification kits.