Can we set up Outlook to be used for email other than a @neiu.edu email address or will no servers there be able to run Outlook at all?
The Microsoft Outlook client which resides on your workstation's desktop and can be configured for all email addresses, not just @neiu.edu.
When the university migrates their email from Microsoft Exchange to NMail, the Microsoft Outlook client will not 'disappear' from your workstation. Servers, per se, do not 'run' Outlook, a person's workstation or laptop 'runs' it.
Everyone who is using a @neiu.edu is encouraged to use the Google NMail interface, as oppposed to Outlook for many reasons. The primary reason being that there is much more functionality offered with Google than with Microsoft Outlook and people would be severly limiting their opportunities by remaining with Microsoft Outlook.
And....Google NMail can be configured to include email from other email addresses people are using. The configuration steps are easily available thru www.google.com.