If at any time the company / IT department think a user(s) of the privately owned network believe that the user(s) is using it for their own (personal) use which goes against the code of conduct contract signed by the employee(s) they have every right to check the account.
We use this at my place of work, due to the nature of it we have to be very careful and monitor everything which can effect our network (like illegal downloads etc). In theory any e-mail sent to a company domain name ([Only registered and activated users can see links. ]) is property of the company as they own the network, the user account and domain name. So any personal e-mails would be concidered missuse but very few companies would fire someone for using it that way.