Are you sure the Outlook on the VDI desktops is setup as POP3 to PST and not Exchange connected with OST cache files? If it is the case that PST files are not being used then you will need Admin access to the Exchange server to dump the mailboxes to PST. Then setup your internal Exchange instance and mailboxes and run a PowerShell import.
If you can gain Admin PowerShell access to the Exchange server you can use this write-up to dump to PST. Start by giving yourself or your login Exchange import/export rights and then skip to the middle of the doc where it says mass export and run the steps from there to dump to PST.
http://www.stevieg.org/2010/07/using-the-exchange-2010-sp1-mailbox-export-features-for-mass-exports-to-pst/
For the discovery/import side of things I like the PST capture tool
http://technet.microsoft.com/en-us/library/hh781036(v=exchg.141).aspx
You can also do this via PowerShell
http://www.petenetlive.com/KB/Article/0000443.htm
Report back your thoughts so we can try and hash this out.