I'm not quite saying you couldn't use fetchmail to import mail, rather that it would be painfully slow. I'm also still fairly new to Linux so I don't know if it could be incorporated but I wouldn't go down that route.
That is a very slow processor you have on that system and way below the recommended spec. Apart from some of the techniques described in the forums for reducing the resources used by Zimbra I don't really know what to suggest other than the obvious, get a new server.
