In my circle, a "meet the baby" party is what parents have when they aren't baptizing the baby. There's always a party after a baptism and that is when people outside the immediate family get to "meet" the baby for the first time. But not everyone in my generation is as religious as our parents, so the meet the baby party is filling that gap of an occasion to honor the new baby.
Also in my circle, the guest list for baby showers, meet the baby parties and christening parties are always just close family and friends. Exactly those people who would most likely be giving a gift to the parents or new baby anyway, party or no party.
So while presents may show up at a meet the baby party, it's not because said party is a gift-grab, but because it is a convenient time to give the gift. I'd say about half the guests at meet the baby parties bring gifts, usually small ones. The other half probably already have given their gifts, as the parties are usually a month or two after the baby is born.