No, what you posted is false:
"Therefore Centrelink can only legally identify one woman as being the wife of any one man" - false
"If a man actually has some more women who are regarded in the community as his wives Centrelink would be breaking the law if they identified them as such." - false
Centrelink can, and does, pay welfare and benefits to 2nd/3rd/4th etc wives and their children.
"Therefore they can only be treated as single women/mothers." - false
