OK, the answer to your fetchmail question is yes you can get the mail with that. As the mail is in individual mailboxes you will need to know the password for each users pop3 mailbox.
Ok, that's effectively an always-on connection.
Turning the server off wouldn't cause you any great problems as the sender should have the mail re-queued to send again if it can't make a connection.
Let me make another suggestion to you that might be more effective. You could host your DNS at a service that provides you with a mail backup store, that means if your server is offline it will queue the mail until it comes back on-line. I use that type of service at easydns.com where they host my dns records and spool the mail if my server is down, it keeps the mail for five days before giving up trying to deliver it. That is, I would suggest, more reliable than mot ISPs mail servers. I have no connection to easydns other than a satisfied user.
