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No. Electrolysing water to make H2 and extracting CO2 from the environment, and then synthesizing hydrocarbons from them, is extremely energy inefficient. Sure, theoretically, it can be done, and maybe one day it could even be done efficiently. But Tesla is making battery-electric cars that work today . The military does not care about efficiency because they have nuclear reactors on their ships and their goal is to…
If they can hit $3 / gallon why does it matter? Tesla's cars are wildly price inefficient because they cost $100K. For 10K you can get a decent car that has 4 times the range. http://en.wikipedia.org/wiki/Tesla_Roadster How many gallons of fuel can you get for 90K? They are nice toys for rich people. Perhaps there is a market for that. Good luck to them. But for mass transit unless you can get the price of the batter…
A mass-produced commuter could be much cheaper, but there's a huge risk. Tesla aims to reduce the risk by validating the market, solving technical problems, creating infrastructure (recharge stations) and solving social problems (convincing people that range doesn't always matter, and educating them on the strengths and weaknesses of electric cars).
A low total-cost (including fuel and maintenance) electric car can probably be produced, but it's not the Tesla's top model.