What IMAP service are you using? I'm using Notes via Google and it syncs between all my iDevices and OS X. And that uses IMAP. So IMAP isn't universally broken. I'm curious about what IMAP service you're using so I can duplicate the problem.
My hosting provider is Lunarpages ....though this is largely irrelevant, since IMAP fucntionality should not depend on one's hosting provider in order to work correctly.
That being said, I don't know the details about Google Notes and haven't tried with it, so I couldn't say. I can only ask: are you sure Google Notes is using IMAP?
As for my Notes IMAP settings: When I open Notes and select the "Notes -> Accounts" menu selection from within the Notes app, it leaves Notes and opens up a System Preferences panel for "Mail, Contacts, and Calendars". Clicking on my desired IMAP account from the list on the left, the right side shows that the checkbox next to "Notes" is properly checked ("Mail" is also checked, correctly). Clicking "Advanced" reveals an IMAP Path Prefix of "INBOX", a port of "993" and the "Use SSL" checkbox checked. Note that these are the exact same settings that worked correctly when syncing notes on Snow Leapord and previous versions. Yet these do not work with Mountain Lion and IMAP notes do not show up in the Notes app.
Note, that when opening the Notes app, it is in fact attempting to connect to my IMAP server, yet does not retrieve or display notes. And, my notes sync and update 100% correctly between my iPhone and iPad using IMAP, using the same server settings as on my Mac. It is only Mountain Lion that has the problem.
As a side note, also note that in order to manipulate server settings for IMAP Notes, such as the server name, one has to do it from within the Mail app; it cannot be done from within the "Mail, Contacts and Calendars" System Preferences pane, nor can it be done from within the new Notes app itself. So it appears Apple was sloppy and did not completely separate Notes IMAP configuration functionality from the Mail app after all.