Yes. A DonorView user can have limited access to events by setting their security settings for events to Attendance Only. An admin user can assign the security settings for a user in the Users grid. Hover over the organization's name and click on Users, then DonorView users.

From this grid, click on the row of the user to modify, then click on View/Edit, then Security Settings.

Under Events, select Attendance Only. Click Save to save your changes or Cancel to return to the previous screen without saving. 

This user will only be able to access the Event Attendance grid in the Events module and they will only be able to see those events and event levels which have been assigned to them under Person Responsible in the Event Setup.