Apparently not. I can't really tell you what my machine specs are. I know it had enough RAM, but I can't check the V-Card since that computer is boxed up at my house and read to send off to Nashville. (It seems lightning ran in on it and destroyed every USB port.)
My suggestion would be you download the latest DirectX version and/or look for a kick ass inexpensive but high powered video card. Quite puzzling since it's a great game.
“Voice or no voice, the people can always be brought to the bidding of the leaders. That is easy. All you have to do is tell them they are being attacked and denounce the pacifists for lack of patriotism and exposing the country to danger. It works the same in any country.” — Nazi Reich Marshal Hermann Goering
It was delayed so that Nintendo could polish it up some more. In all likelyhood, TP will be the last great Gamecube game, and they don't want the 'Cube to drizzle out and die a slow painful death like the N64 did.