Visual Voice is used with both Embedded Voicemail and Voicemail Pro. We would really need to know which you have.
If you have IP Office 9.1, then in Visual Voicemail you can have indication of messages in other users mailboxes. No need for a hunt group mailbox. Uses a U character followed by extension number in the user sources numbers if I recall correctly. So not only would they be able to access each others messages they would have some idea of who the message was originally for. Practicality might depend on the number of users you are talking about.
If not on 9.1 or the above doesn't appeal:
On Embedded voicemail then the answer really is no. Can't automatically route messages from individual mailboxes to group mailbox so no user greetings. Can added group mailbox to Visual Voice using the tradition H character option in the user source numbers.
On Voicemail Pro, you could create a custom callflow module that is then added to each users Leave start point. It would play a greeting file specific to the targetted user and then put the record message in the hunt group mailbox.
Lets us know which voicemail you have and the number of users (and whether this is for all users or just a subset)? And depending on your choices of solution from the above and the other answers from others we can be a bit more specific about the configuration.
Stuck in a never ending cycle of file copying.
