Can the network administrator for Outlook view my emails?
Yes they can. Remember that the company you work for owns (pays for) the rights to the entire network, all of its equipment, etc. They also supply the connection to the internet. The network administrator can view but it’s usually the e-mail administrator that gets the joy of monitoring e-mail usage and enforcing company policy if needed. The computer and its connection are supplied for you to use while you work. Sounds like this might be an issue of perceived invaded privacy. If you don’t want anyone to read your PERSONAL e-mail at work, don’t use their stuff to send and read it. Do it at home.