I'll admit that I probably am misunderstanding your question, but if you're running Evolution, once you d/l your mail (while you are online) it'll just stay in your Inbox until you either move it to another folder or delete it. There's no requirement that you actually be online in order to read Email in your Inbox, so once it's been downloaded, it can be viewed at any time, online or offline. Additionally, once you click on the Send/Receive button to start the retrieval process, you are free to open another browser, etc, while your Email is collected.
Are you asking if it's possible to set up some kind of cron job to automatically connect to your ISP, login, and get your Email? (If so, this would be beyond my ability) -- J.W.