There is no mechanism to communicate with a client and give them this information built in. There is also no need to poll over AMI for the information though. If a connection is kept up then events[1][2] will be sent when people join or leave the conference. You are then free to communicate with the client however you wish.
[1] https://wiki.asterisk.org/wiki/display/AST/Asterisk+13+ManagerEvent_ConfbridgeJoin
[2] https://wiki.asterisk.org/wiki/display/AST/Asterisk+13+ManagerEvent_ConfbridgeLeave