I will preface this answer with, I have never done this before so I don't personally guarantee that the scanner software will work in a shared environment.
But with the being said I do see some devices that claim that they can share USB device such as Scanners between multiple computers.
here is one example of such a device
Here is another example
What would worry me about the validity of all of this is if it is a valid solution, and something I am sure alot of people could use, how come the big boys in the USB market like Belkin haven't made a device that does this?
Also really since someone has to put the document on the scanner anyways why not just use one station as your actual scanning station that has the software and what not and just save the scans to a network share that everyone on the network can access? Just a thought of a potential work around for you.
PS - Also just found this software that claims to do it.
http://www.remote-scan.com/remote-scan-purchase.php
sorry I know this wasn't the most clear and concise answer but hopefully it has helped point you in the right direction