I don't know about Google for Education, but the business flavor doesn't let you spy the email of your users, at least I haven't found it. There are ways that allow you to copy every email to an "audit" address, if you're persistent enough, but good luck managing that mess and liability.

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.