Can inc download gmail through imap?
No. It's designed to retrieve messages from a maildrop. And POP
provides a maildrop; IMAP is really about providing remote access to a
mailbox. inc works fine with the GMail POP interface.
The obvious answer to IMAP support for nmh is just treat it like another
mailbox so you wouldn't use inc with it, you'd use all of the other nmh
tools on it (because they're designed to deal with mailboxes). I have
a workable design for this; I just wish I had time to implement it.