No..As soon as the "script" (and thereby the session) from one browser is "transferred" to another browser, the session on the first browser is expired. So effectively only one user will be running the the script at one time..There is no "sharing" of a script state/session. Only "transferring" of the state.
The intention is to achieve a "one click" transfer. So say agent A is answering the script in his browser. Midway he finds that this script needs to be transferred to agent B for his inputs. So he presses a button and voila, the same script session is transferred to Agent B and is opened in his browser and Agent B can complete the script.