After the baby is born! Make sure that 72 hour window has passed and the birth mother has signed her parental termination papers because it will be a painful situation to have a party only to find out at the last minute that the birth mother sees her precious child and changes her mind, keeping the baby.
I wouldn't invite the birth mother unless you think she is totally down with it and absolutely can handle it. Remember, it would be a party for the adoptive parents - the ones who didn't carry the baby for 9 months, the ones who didn't agonize over whether placing their baby was the right decision or not, the ones who will be showered with all the gifts and affection. It might be very difficult for the birth mother seeing the adoptive mother get all this attention heaped on her while the birth mother gets "You've made this couple so happy!"
Consult with the adoptive parents and see what they think about the timing of the shower. I totally get what you're saying about having everything ready for when the baby comes home. If they can handle it emotionally, then definitely honor their request.
Above all, I think you and your friend are simply AWESOME for wanting to host a shower for the adoptive parents. Thumbs up to both of you!