Does anyone know if it is possible to get outlook (partially) working with an exchange service with only makes Webmail and ActiveSync publicly accessible?
I don't believe this is possible. Outlook uses RPC over HTTP(s) for remote access. This requires a separate configuration on the Exchange server, its not part of OWA or ActiveSync. I don't think there are any full mail clients that work with Outlook Web Access or ActiveSync.
I do seem to remember a taskbar app that would notify you of new mail that it saw in OWA, but it wasn't a client, just a notifier.
What are you trying to do?