Actually, they might sue you. You would have to get into a marketing program and they would have your car wrapped or painted and I am sure pay some sort of incentives for driving around in a mobile advertisement, however if you do it yourself, with out prior consent and a contract from Google, you have a very real chance of being taken to court.
No they will not. Google requires people to get their permission or consent when using their logo. They do not allow any of their brand features to be edited, altered or misrepresented and their use might get you in a law suit.
they would sue you because first you would have to get into the marketing program and allow google creators to be noticed if you drive around with its logo you have a very good chance of paying the company a fine up to about $12,000. i wouldn't recommend it. :)