We had a fun engagement party thrown by both sets of our parents at a restaurant (that had karaoke). We sent out an evite, so it wasn't a very formal occassion, but we did invite people who weren't invited to our DW. We are having an AHR when we return, so everyone who was invited to our engagement party was invited to that as well. Having said that, we didn't invite a ton of people to our engagement party. I would say we only invited 5-10 who are not coming to our DW.
All of our friends and family knew that we were trying to keep our DW very small and intimate, therefore weren't inviting everyone.
We did not register before our engagement party (and actually still haven't registered) because we didn't want people to bring us gifts. We actually put on the invite not to bring gifts. That is just our feelings though. I think you can do what you want!