This would be inconceivably stupid. Work email, particularly .gov email is snooped a lot closer than private email. If you don't want your private email snooped, you set up another private email address.
Email verification was never required to sign up to Ashley Madison. An email address was requested to sign up but it didn't have to be a real one. You could sign up with a fake one, or someone else's email address if you wanted.
But, I'm sure there are plenty of real accounts, and I have no sympathy for those people. Anyone in there who has a security clearance should be taken to task over it, as well as anyone in any trusted position.