It is possible. I was able to charge a Jeep onto my SPG card, but they made me pay a fee. (which was OK cause add that to the first purchase bonus, I got some nice upgrades on airlines) and since I paid it all off at once, I was able to get a lot lower cost on the car (basically dealer cost + some freebies) So at the end, it was cheaper to pay it on the card, even with the fee.
Technically the fees are illegal, but then the dealer might not take the card at all. I would search around you area, then check sites like vehix or carmax.