Let me see if I understand what you're asking. You've got a VI that you will be running on a computer that has both a monitor and a projector attached to it. You want to know if this VI can determine where it is being viewed and chang its background accordingly? If so, you can't actually do this. The VI itself can not determine where it is being displayed.
However, if you are looking for something else, let me know and we'll try to figure something out.
J.R. Allen