No, SMTP servers just route mail by default. There will probably be evidence a mail was sent, the sender and recipient addresses, the subject, and maybe its size, but not it's contents. That is, unless you have a mailbox on the server. If you have a mailbox on the server and it is IMAP or Exchange it would store in your mailbox sent items. With Exchange, if you delete an email, it goes to the soft deleted items cache and sits there until the garbage collection process permanently deletes it. Usually this is 30 days later. However mailboxes can be placed in legal hold where no mail is removed by the garbage collection process and no one can delete it permanently. Also there are mail database backups to consider.
But you mentioned POP3. By default, POP3 is a client managed system: your mail client downloads the email and it is removed from the server. Sent email is stored on the client and not the server.
That said, POP3 can be configured to NOT delete email when a client downloads it. Even then, sent mail wouldn't be stored on the server.
You should be okay if you are trying to hide sent mail from your company, though I would recommend using a service that doesn't involve your work at all to be sure.