Technically, no. The reasoning is that a registry is there as an aid to your guests. I want to get you some towels, but I don't know what color matches your bathroom (or whatever), so let me go check your registry. You don't include registry information with the invite because then it would be seen as asking for gifts. But money is universal, everyone likes money and everyone will gladly accept it. It doesn't really come in different styles or colors with different features, there's no need to register for it. Creating a honeymoon registry is just saying "GIVE ME MONEYYYY PLEASE" which is a big no no in the etiquette world.
At least that's the justification behind it.