No, it’s not possible unless you have their passwords.
From my moonlighting jobs and previous jobs I usually include myself in the SysAdmin or IT email groups or distribution lists. I received a good one yesterday (translated from Malay):
Dear IT, Need your help to delete 3 emails sent by John Doe to 3 recipients below because we sent the wrong email to the client.
There are different headaches in maintaining email servers, for example one might complain of too many spams but sometimes “valid” emails gets filtered. But this one really made my day.