It depends what you mean by "in sync". You could leave every message on the POP server and have both clients download everything. But your POP server provider might not like that. That's the only way to be sure that both clients will have the same messages, though. There's no way to set up your POP server to check to see if all of the clients have downloaded the message and then delete it from the server. (I mean, it's technically feasible, but no one's done it.)

A better solution might be to have GMail (or some other mail service) download that POP mail for you.

Personally, I'd set up or find an IMAP server somewhere that could download the mail via POP and re-present it to your two clients.