One of the stated purposes of this tool is to "liberate your emails" by letting you keep local copies of every e-mail you send and receive. If you need to use a third-party IMAP server to keep a backup of your e-mails, how does that liberate you? Now you're dependent on two online services instead of one.
Reading locally stored e-mails would be a problem for non-geeks, though. But I think the right way to solve that problem would be to offer a program to read those e-mails, or even better, a plugin to a popular mail client (such as Thunderbird) so that the e-mails can be accessed through the mail client. Depending on the "cloud" just detracts from the stated purpose of this tool.
That way, if your google account goes away (I guess we all agree that administrative account lockout is way more likely than google actually losing data) and you need an email RIGHT NOW, you would just configure any imap client to use the daemon provided by the backup application (localhost:143)
Or it could bundle some web based mail client and then open a browser.
It's impractical to reupload the whole backup to gmail before being able to access your mail.
But now you've got a background process running on a privileged port, yikes! (It's got to be a daemon that starts automatically, because "non-geeks" will not understand why they have to start another program before accessing their mail in Thunderbird.)
I think you're misunderstanding pilif's comment. That "small IMAP server" would run locally on your box, which gets you to the goal of having any standard mail client read the archive.