Playing fullscreen video when starting the ipad-app?

Do you mean an avi/mpg,... video or a Unity3d Scene with camera?

For both: Just create a label(Or Cube) and assign the video as texture. Now just set the cube to the size of the screen.

You can use Screen.height or Screen.width

Hope it helps u

Have you looked at this question: http://answers.unity3d.com/questions/11312/how-integrate-video-before-menu-in-unity-iphone-game

If you mean use a video as a splash screen for your app, you can't do that on an iPhone/iPad. After the app has started you can set up a scene that plays a video if you have unity ios pro. If not, you need to play the video using Apple's own mechanisms.