Whether or not you can do that depends entirely on the sync software you use.
Outlook does not take an active part in the sync and there are no settings
within Outlook what can control the sync. Ask your Blackberry vendor.
You could set your second computer to use the same exchange mail
account. But if you dont what to do this a solution would be to use
Dmailer sync on a usb device to synchronize first with your exchange
server then you can synchronize the data on the key with outlook,
outlook express and windows mail or send and receive emails directly.
Note Dmailer Sync is not free but I don't think you will find free
software to do this type of synchronization any other way.
To download this software you must go to the Dmailer Website:
http://www.dmailer.com