Down here I know you can have a motor on a bike but it must be below 50CC. This is why it is common to buy the ebay 49cc bike engine (has 49cc cast into crankcase) and use the larger piston, barrel and carby.
Having said that it'd be poor form for a cop to give a young bloke a ticket for having some nostalgic style. From what my old man has told me of the old bike engines weren't fast but sure would make it easy to drag mowers home. Could even make a period style oiled timber trailer for bike.......

This
Is going straight to the pool room.