A user wanted to know if he could access his Exchange 2010 archive mailbox using active sync.
No, its not possible. Although the archive mailbox is separate mailbox and some mobile devices support multiple Exchange accounts, it is limited to primary Exchange mailboxes, not secondary mailboxes. Plus, it's not very efficient to load old messages on a device with limited storage space and limited bandwidth. If you need mobile access to the mail, don't archive it.
For more information, see TechNet's Understanding Personal Archives