Is there a full-featured Mac email app that natively implements labels (instead of folders) and archiving?
I have two backup recommendations. Although these are not apps you'd use to manage your mail, they do backup your account to your system so you can use whatever management client you like (e.g. Sparrow, Mail, etc.). 

I use getmail by Charles Cazabon to back up my entire Gmail account silently in the background. The emails are backed up into a large .mbox file, accessible by any number of mail clients. This also makes it easy to move your entire account from one machine to another, or to restore. The program says it works with any IMAP account - support folders, labels, etc. I only use it with Gmail.

A second backup option is Gmvault. There's a Windows GUI installer but for OS X one still needs to go to the command-line. Again it backs up your Gmail account (the sync option) and stores the emails locally on the file system. Emails are stored individually as .eml with an accompanying metadata file. You can manipulate those files as you like without messing up the gmvault functionality. There's also a restore option, and it's suppose to handle IMAP discrepancies with Gmail well, although I've never encountered any problems there that (of which I'm aware).