All persons born or naturalized in the United States, and subject to the jurisdiction thereof, are citizens of the United States and of the state wherein they reside.
That explicitly defines citizens as people who are born. I'm not sure Georgia gets to add a whole new category of citizens.
The Georgia law doesn't address the question of citizenship.
Please understand what I'm up to here. You're thinking of things that are occurring to you, and that's a great place to start, but I'm encouraging people, you and others, to go beyond thinking about things, and speculating, and connecting the dots in any way that they can with the limited information available to them and, instead, go out and find the actual words of the actual law and see if they match the ideas that occur to them. In some cases, things are vague and it will be up to the judge that hears the case. In other cases, the law is absolutely crystal clear.
That specific line of the constitution was indeed cited in Roe v. Wade, but not with respect to citizenship, and the Georgia law doesn't deal with citizenship. It deals with personhood.
But even if the questions were, what does that line in the constitution say? And does it help us see how to interpret the law?
It says, "All persons born ... in the United States, ..., are citizens..."
So, people might remember this one from philosophy or logic classes.
All persons born in the US are citizens.
Fetus X has not been born (in the US or anywhere else)
Therefore...…(the conclusion is left as an exercise for the reader.)
And the practical implications are just creepy. Is the state of Georgia going to keep a database of pregnant women in the guise of protecting the unborn? Will women be required to report their pregnancies to the state? Will miscarriages need to be independently evaluated to rule out foul play? Will death certificates be required? Are birth certificates going to be supplanted by certificates of conception?
I agree it is kind of creepy. But why would any of the things you asked about be true? There is an actual law with actual words in it, and these questions can be answered there.
Database? No.
Pregnancy reporting? No, but see below.
Miscarriages evaluated? The law makes no provision for this, but if there is suspicion of a crime, i.e. a suspicion that an illegal abortion has occurred, then it ought to be like every other crime. There's a lot of discretion involved on whether or not to investigate, but I can certainly imagine this happening.
Death certificates? They are already required under Georgia law. In the case of fetal death or of induced termination of pregnancy, paperwork is required.
Conception certificates? No.
Could future legislation change any of the above answers? Yes. Indeed, as someone pointed out, we can expect if Roe is overturned that this will be only the first step in the war against abortion. First, they have to get Roe out of the way.
One thing that I am fairly certain would be true is that a woman who has a miscarriage after six weeks or more would be entitled to claim the fetus as a dependent for tax purposes. The law seems fairly clear on that part.