That will work if you replace the initialization of m_client in Webserver.h (ArduinoConnectServer/WebServer.h at master · milocreek/ArduinoConnectServer · GitHub):
instead of:
m_client(255),
use
m_client(),
I've no idea of why they used this (undocumented) constructor as the standard no-arg constructor defaults to the same value, so it wouldn't make any difference for ArduinoConnectServer. (I also have no idea of why this constructor is not decleared private in EthernetClient.h as the argument refers to a WIZ5100-internal register, but this is another story).
P.S.: I just opened an issue for ArduinoConnectServer, so the author might want to change this: