Please note that this site is now out of date and has been replaced by Google Workspace: a Practical Guide. If you came here from a link, please update the link accordingly. If you have any questions, please email itsupport@york.ac.uk FAO the DISC team.
You can use YouTube with your York credentials.
It is not not fully integrated with Google Apps meaning that you can't limit access to "Everyone at the University of York" or people in your department.
You can however make your videos only available to people who are given the link. This can limit access but doesn't prevent people from sharing the link more widely.
An example of using YouTube, which integrates with many video editing / mobile applications might be the User Stories from people using Google Apps at York.