I think a receiving line could work for an engagement party *if*
- the party is large (minimum 50 people)
- the party is reasonably formal (thick formal reception, not cocktail party)
- people will be arriving in a fairly narrow window of time (ie, not a drop in or open house)
- the party is held at a venue where there is a lobby where people can stand while waiting until they are received (not outside the front door of your house) and their coats can be collected and checked when they arrive.
- the party is being managed by a staff that can take care of your guests during and before the receiving line (collect coats, serve drinks and food, direct people to the washroom, pick up empty glasses and plates, etc)
Then, a receiving line would match the formality and organization of the party. Asking guests to huddle outside in the rain until they can be received, and then having them mill around the party on their own until you are finished wouldn't work.
I did a quick bit of searching for non-wedding reception lines, out of curiosity, and what I came up with was funerals, political functions, large formal parties held at places like country clubs, cotillions, and military receptions. For funerals and weddings, it's done as people leave the ceremony, all the other events are held at venues with staff to manage the party.
Addresses mixed families and the receiving line.