Removing (deleting) Email Notification Templates will cause the associated builds to fail until the job is updated to reflect the template is no longer to be used.
Steps to reproduce:
1. Create two Templates in Email Notification Templates
2. Add both Templates to a job, and run job, see success
3. Edit Email Notification Templates, and remove on of the templates
4. Run job again, See error
The Job should not fail because of a missing template, but it still might be good idea to bitch that there is a missing template and then remove it?