I think it all depends on the expectations that you set with your interviewer.
I do not think you would be looked at "quizzically" if you arranged it with them beforehand. The reason is that they would expect it and they know it will happen. They might even want to help you out with the cabling and providing a bigger screen.
Suppose that they did not expect it, so you just whip out your laptop at the time of the interview; then there exists the possibility of a "quizzical" reaction. The interviewer will probably also just say "no" and force to solve the problem on a whiteboard.
At the same time, I think that the point of a whiteboard question is not to test syntax and speed, but rather to evaluate problem solving skills. There's a different criteria that your interviewer will look for that simply checking "how fast you write/program".
Also consider that you might make it harder on yourself by taking a laptop with for code writing. Your interviewer might be less lenient on you because you're in your ideal setup, so making mistakes might count more. They might even add more criteria than a whiteboard evaluation because of this.