Sure. One note...meant to say it before...but my brain was tired (it is a sad state of affairs when you can't brain at 8 am...)...just having a teacher-ish role will not necessarily receive a notice of work submission. Even a full on teacher might not receive notice. In theory, some activities (assignment specifically) will notify someone of a submission. It isn't always the person you expect. I used to have a course I was assigned a teacher role in. I also had a small chunk of people with site access who were students in the course. Assignments would get submitted and notification would go to those people not me (for no apparent reason). It was crazy. I never did figure it out. The lesson: don't give people site access. Well, maybe that is the lesson.
You're better off having the non-editing teachers check into the courses they need to monitor a couple times a week. Hopefully, it isn't a huge number of courses. Forums will email subscribed users--but all subscribed users, not just the instructors. Well, maybe you just subscribe the instructors?