Is there anything I need to install from the DVD or will the launcher patching take care of everything?
Actually, those 800 MB probably DID appear because you typed in the key. However, the launcher has no direct access to your account info, and so, does not get updated (and thus, told to connect to Battle.net and download Cataclysm data), until you've logged into WoW after upgrading your account. Hence, you began downloading data the second time you opened the launcher.
And no, you don't need to install from the DVD, but keep it around in case you ever need to reinstall: It's a lot easier than downloading the entire game!