I just wound up doing a bit of research on this for other reasons.  Piers Lauder was the original author of the imaplib module, and he is (as far as I can tell) currently maintaining an imaplib2 module that does support IDLE (but not, I think, python3).  But it does IDLE (and other things) via threads, and in the email I found announcing it he didn't think it was suitable for stdlib inclusion (because of the threading).  Piers hasn't contributed to core in quite a while as far as I can tell, but he was active in a bug report back in 2008 according to google, so I thought I'd add him to nosy and see if he has time for an opinion.