Run app as a different user (automator)
You can not trivially launch graphical applications as another user.

A Proxy Process is Required

To launch a graphical application as another user, that user must be logged in to a graphical session and have a process running within their session able to launch your desired application.

Prior to OS X 10.9, this could be approximated via the launchctl command. See How to launch a GUI application in another user's graphical session? for a detailed discussion.