As of the May 2016 release, the IE Native Browser Agent does not require Windows administrator permissions. Any DOMAIN\user account that have logon access to the local system can use this agent. 

However, the Internet Explorer browser cache is shared with the user account that is configured for Private Last Mile. If that user frequently uses Internet Explorer on the machine where Private Last Mile is installed, the user's updates to the cache and the IE Agent's clearing of the cache may cause varying results in the Private Last Mile data. Therefore, we recommend assigning a dedicated user account to the private peer.

For users that can run processes on the machine but have no logon access, that is not officially supported by the IE agent thus you will much likely see test gets to run but blank pages displayed. Simply grant logon access to the user and test should be able to run.

Any further questions you may have, feel free to contact the Support team by opening a ticket.