In certain respects a good idea, if all you want to do is pay for the entire car with a credit card. However, I'm fairly certain that once you show the dealer your intention to do so, if he agrees, he's definitely going to factor this into the cost he's willing to sell it to you for.

If the only reason for paying with CC is for the rewards, then I wouldn't tell the dealer about my intention to use the CC at all. Negotiate your best deal, and then when it comes time to pay, whip out the credit card then. Put as much of it on the card as they'll allow. If you want to go through the extra effort, try speaking with the manager to put more on the card, or try quoting their merchant agreement with them to put the entire purchase on the card -- expect a lot of push back, or to walk away from the deal if you insist on going that far.

I've often thought of doing this, but, don't plan to buy a new car any time soon: order a bunch of $1 coins from the mint, pay for the car in coins.