Looking around the web it seems that this issue with GoDaddy and IMAP push seems to be annoying multiple folk on all platforms. They still pointedly refuse to support IMAP push to anyone, anywhere.
The best answer anyone could come up with was to poll often. Not even remotely ideal I know, but it looks like GD really want you to pay for their Exchange hosted services to get push mail.
Granted polling ain't the best solution for bandwidth reasons, but have you thought of using another host, say Gmail, that would poll for you then push what it finds? True it's a bit of an ugly solution if not fully executed end to end in an organized fashion, however it's how I handle email with 1&1 and Google Apps (however I did a lot of work behind the scenes to join the two).
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