What is this non-shower BBQ being called? What are you inviting people to attend? Is this a "Come celebrate that George and Martha are having a baby! BBQ at 5," or "Martha's having a baby and we're having a party!"?
If it is not a shower, don't call it a shower. The problem comes that there really isn't a simple term for a party to celebrate a pregnancy without gifts that everyone will be familiar with. I would be very careful with the wording on the invitation to make sure people realize that it isn't a shower. And I'd be very careful about how the party was talked about--no hint or mention of shower, gentle reminders that the Guest of Honor doesn't want gifts, telling people who ask about a registry that the GOH didn't register on purpose because she doesn't want gifts, etc.
I think that if you don't call the party a shower, then you are technically in the clear about opening any gifts that might show up after the party and not in front of the guests. Only at showers, and children's birthday parties, is the gift opening the main event, so to speak. Everyone involved should do a lot of talking about the party, "Oh, Sue and Sam don't want a shower. But they do want to celebrate! So they are having a non-shower-type party--everyone's invited!" Just because someone brings a gift to a party does not mean that the gift has to be opened at the party--just as a hostess gift of food or drink at a dinner party does not mean that the food or drink must be served at that meal.
This doesn't mean that people won't bring gifts. And some of them may be upset that their gift wasn't opened in front of everyone. But if they were told the party wasn't a shower, then they need to deal with their upsetness by themselves.
But it might be easier, in terms of gifts, to wait until after the baby is born and then have a "Welcome the Baby" party. Because I think a lot of people are going to hear "party to celebrate a pregnancy" and think "shower" and "I guess I have to bring a gift."