The short answer : Yes, you can train the coin pusher with real money (coins) and play with for instance Euros or Dollars. Should you do this ? Well, that greatly depends on the local laws. In most European countries it is not legal to play with real money unless you have a gambling license. When you use tokens (you can order these with your machine) you are usually good to go as these are not legal tender. Coin pushers usually have exceptions in the law that make using them a lot easier as they are regarded as fair-machines and not strictly as gambling machines.
Moral of the story : Check your local laws and order tokens with your machine.