Will using IMAP download all my mail?

Not unless your client is set to do so. Most IMAP clients will download only the headers of your Gmail messages while you're connected to the Internet. However, a few clients will download all of your mail by default.

Your messages will download completely when you select your client's option to work offline. You'll be able to read, sort, and compose replies to your messages while you're working offline. Once you're connected to the Internet again, you'll be able to sync your client with the Gmail interface on the web.