You could in theory do that although the experience would be slightly odd. Either open the video in a new page and put in the bottom right, force focus it after the main window been active. Or wrap the entire websites in two iframes, one for main content and one for video player. Main content can change without interfering with the video player.

Not saying you should do either of these, as the UX would be worse, but you could if you really want to :)