Wow, replying to my own message, sorry for the noise.
On Fri, Mar 21, 2014 at 05:11:36PM +0000, Adam Thompson wrote:
> Given how many linux clients support imap (including a very ed-like email
> client) I'd be very surprised and disapointed if a decent library isn't
> available for this.

From the output of apt-cache show libcurl3:
libcurl is an easy-to-use client-side URL transfer library, supporting DICT,
 FILE, FTP, FTPS, GOPHER, HTTP, HTTPS, IMAP, IMAPS, LDAP, LDAPS, POP3, POP3S,
 RTMP, RTSP, SCP, SFTP, SMTP, SMTPS, TELNET and TFTP.

Hmmm, looks like we have our imap (and smtp and pop3) library,
and it does ssl as well, unless the description is incorrect.

I'm not sure how it's imap support works though.

Cheers,
Adam.