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Get started and then sit back and wait.

If the connection is lost in-between, would the download resume from that point?

Yes, because it's not just one file but thousands of individual messages. If you start downloading by POP or IMAP it will bring down the individual messages, so if you get stuck in the middle it will resume (after some waiting time to figure out what's not transfered). It only takes a long time once and then should be hardly noticeable.

Google is OK with you doing that, they'll eventually throttle down your IMAP connection, but it'll keep going.

You could use Imapsync and a VPS somewhere running an IMAP daemon. Then it's easy to sync back out to another email host if you hit trouble with Gmail