The topic here is signaling. The large and colorful tail of the male peacock tells the female peacock about his strength and virility (if I can run around carrying this large and difficult tail, just imagine how strong I am). In the same way, we humans are concerned with the signals we send the people around us about who we are. Signaling is part of the reason we buy large homes, dress up in designer clothes and buy particular cars. So the answer to your question is yes. The car that you drive communicates something about you to the world. Does it matter? Yes again, because we are experts at reading these signals and making inferences about the senders.
But some questions remain. What kind of signal do you want to send? The BMW signal or the Prius signal? Maybe the signal that you buy American-made? Maybe you want to get a really old car and show people that you take really good care of it (a more subtle signal, but an interesting one). Another question is whether the cost of the signal (the cost of the car) is worth its signaling value. This depends on the nature of the people you deal with, how well they know you, how often you make first impressions, etc.
In the interest of full disclosure, I should say that I drive a minivan—but now that I am thinking about it, maybe I should go and stick a Porsche logo on it.
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