"Meet the baby" parties are the norm in my social circles and culture.
We do not have the concept of "baby showers" - we just don't know it (first I ever heard about such a thing existing was here on this site).
When I was little and going to church was the norm, the norm was that the celebration for welcoming the baby by friends and family, was the baptism festivity. Now that the majority of people (at least the ones I usually deal with) are no longer involved with church, this celebration has been replaced by a "meet the baby party".
People here do a lot worse things than you do, though. Many include a registry and/or a "diaper account" - a bank account in which people can donate money!! I think /that/ is rather tacky - but most people here think even that is normal. Worse, even: some include the registry and the diaper account number in the birth announcement card they send to people who are not even invited to any sort of welcoming party!!
Your scenario would be fine for me. I /would/ bring a gift, gladly - I just don't like to see it mentioned on the invitation / card as if the parents take it for granted or directly ask for it, you know? But no, I have no problem with yours.