Until finish converting this article from the other site, the short answer is no. Theres a bunch of tests I did one Saturday but the simple explaination is that black cars get hot faster. You would notice this if you get in and out of your car many times a day but if a white car and a black car are in the beating sun all day - the cabin temp would be the same. Yes white is cool to the touch but the big heat collectors are the windows. "I have a solar windshield covering thingy" you say. That just keeps the excessive heat from the DIRECT sun off of your steering wheel but still fills the car with the hot air generated between the glass and the fabric thing.
Oh, and example of direct sun heating vs ambient. Ambient is the temp of the air around you, direct is the heat that the light radtion interacting with the materials surface. An perfect example of this is resting and burning your arm on an iron gate on a sunny day.