If you cancel & still expect to get still read those messages, then No. I would suggest either downloading the messages to a local email client or forwarding them to another email address. I believe once you cancel (or when the cancel order is processed), the email address is deleted & all emails, contacts, etc are deleted also
said by JRA :
We have switched to another provider, but have not cancelled our Qwest DSL since there are still messages we need to get off the server. If I set up an Outlook account to pull those messages over, will I still be able to access them in Outlook even after we cancel the DSL?