At some clubs, yes. Most will just politely notify the offender that push carts are not allowed, and that he must carry his bag/take a caddie/jump in a cart/whatever policy allows. That's sufficient. Golfers in the US are nothing if not dignified. Honestly, I've been a member of three clubs in the US, none of which allowed push carts, and I've never seen the rule broken at any of them. What do clubs in Australia do to enforce their club policies?