Perhaps WebMeeting's private room capability would be better suited to this.
1) WebMeeting URL opened in browser at all times.
2) User enters his name and presses login.
3) An extension or queue with agents receives a chat and/or email notification about a new visitor waiting in a meeting for him. This notification contains a link to join this temporary meeting.
4) An agent joins the meeting, talks to the user and either side can end the meeting at any time.
The cool thing about this is that any user who clicks this URL, enters his name and logs in gets redirected in his own separate private meeting room. Agents in a queue then join and serve these users.