Activesync/OWA Desktop Client

I think DavMail should be able to solve your problem. To quote from the page

Ever wanted to get rid of Outlook? DavMail is a POP/IMAP/SMTP/Caldav/LDAP exchange gateway allowing users to use any mail/calendar client (e.g. Thunderbird with Lightning or Apple iCal) with an Exchange server, even from the internet or behind a firewall through Outlook Web Access.

It will provide POP/IMAP/SMTP/CalDav/LDAP backends to an Exchange OWA gateway.

... You just got me thinking, Why doesn't Outlook support Activesync! I guess it would just be a redundant feature for Microsoft to support when RPC is so much more feature rich and complete...

A quick thing that may work is just to set up a rule on Outlook (if you use it) or through OWA that will forward all your emails to the external Gmail account.

Another thing may be to beg your administrator (or bribe with Pizza!) to enable POP3 or RPc over HTTP, even if it is just for your IP.

Anyway, Sorry I cannot really think of a proper easy solution, I cannot find an PC Activesync addons - Other than downloading a Pocket PC Emulator!.

Outlook 2013 now supports ActiveSync natively (no Hotmail connector); however, there appear to be problems with non-Hotmail connections.

The built-in Windows 8 mail client also supports ActiveSync connections.

Edit: It looks like Outlook 2013 will only support ActiveSync connections to non-Exchange servers; see Exchange, EAS, and Outlook 2013 for details.