The Web Service utilizes the same connection/authentication mechanism as the Web admin GUI - same management port, same authorization layer. As far as I know, we don't support client side certificate verification in the GUI so it won't likely work with iControl. I'm not saying that it can't be done, just that as far as I know, we don't support it and we haven't tested it. I'd check on ask.f5.com to see if you find any solutions around setting up the Web GUI with client cert authentication. If so, then iControl should follow the same configuration.
-Joe