IMAP (or IMAP4) is a common alternative to to POP (or POP3), and would work the way you want. I don't know if Yahoo supports IMAP however, nor do i know whether you'd have access to those e-mails without an Internet connection. With POP, e-mails are downloaded to your device, so you'd be able to read them with or without an Internet connection.
There may or may not be an option on the Tab to leave messages on the server (after downloading), or delete them once they've been downloaded. I don't use POP, so it's hard for me to say.
Look for instructions on yahoo.com for setting up IMAP e-mail.