Yes, you can set up your events so that they are automatically removed from the schedule once all slots are taken.  (Please note: the exception to this would be if your event has a user group reservation in place.  If a user group reservation is in place, then members of that group will see the event, regardless of its status.)

To do this, simply apply the Event Visibility option to the event, which makes the event disappear from your list of opportunities whenever the Sign Up button is not available to a volunteer. Since the Sign Up button is always removed automatically once the event is full, enabling that option will remove filled events from your schedule - this way volunteers will only see events they can actually register for. 

Step 1.

Navigate to the Event or Master.

Step 2.

Click Edit.

Step 3.

Scroll down to the Registration Details section and choose the Event Visibility option of "Hide this event when registration is disabled."

Step 4.

Click Save.