Some things I have learned:
1) Be very aware of the content that you include for them to send out. Generally, I made emails available after the event had passed or once something was published. IE--I only made webinar emails available after the recording was available, not for the invite. The reason why I ended up doing this was because there became an issue with reps accidentally sending the invite after the webinar was over if I didn't remember to take it down in time. If you're a a smaller marketing team, this may be a good approach to avoid any issues/hiccups.
2) With #1 being said, #2 make sure the emails are clearly labeled. Also a monthly audit of which emails are available in insights in also helpful and helps to ensure accuracy.
3) To answer your question about those being tracked: we tended to track only lead generation focused emails. Although rep intro emails and event emails are helpful for reps, in the long run it didn't seem as though they were worth our time tracking since they were more of a 'nice-to-know' vs. a 'need-to-know'. I would also think that most customer service emails wouldn't need to be tracked either, although I've never enabled a customer service team to use the outlook plugin.
Hope that helps!