Yes. 

If the event or event role the volunteer signed up for is canceled, they will get a signupConfirm notification letting them know.  Depending on the user's notification permissions, this could be sent as an email or SMS/text message (or both).  For recurring events, we will only send out cancellation emails for events in the upcoming 90 days.

Users/Volunteers can change their permissions in their profile under Action then Settings.  There should be a Manage Permission link.  Having a phone number on their profile will enable the SMS/Text permissions to display and be configured.