Yeah of course, gsuite administrators can access everything, and because gsuite admins are just modern-day instances of bofh-type obnoxious IT guys, there's no way you'll convince them to give up those powers.
There's the option of quarantining emails that have specific keywords. That's the likely way to catch students discussing cheating, attachments and all.
Edit: as the comment below has pointed out, this might not be true. Different editions have different tools, the one i use is not the most complete.
Email routing is also an option, although far more heavy handed.