I have a user who is in the office 2-3 days a week. When he's not here, his computer is off. He has his Gmail account setup in his Outlook 2007 via POP, and when he comes in to the office, Outlook does not pull in messages that were recieved when the machine was off. His phone and iPad recieve the messages, and they remain present on the server.
I have the POP 'Enable for ALL mail' set in his Gmail, but he's still not getting the older messages (he did when I initially set it for ALL). He does receive new messages when the computer is on though, so that's working.
I have my Yahoo account in my Outlook, and I always get old and new messages.