There are only 2 real states at the moment: Open and Closed. Beside you can define custom status in the Admin Panel but these must have one of the two base status (open or closed) and as far as I know these custom status are only visible in the admin panel and not in the end user web portal. (correct me if I I'm wrong)
So beside modifying the core files or responding to the user to tell em that an agent is now assigned the ticket, I don't see a way to inform the end user.
Sure there is the possibility to automatically assign a ticket and send a canned response thru the ticket filters or the help topic options, but I guess you don't want to automatically assign all tickets that way so I mentioned it now but left it out above in the response to your actual question.