These are good questions. I would like to emphasize that I don’t think we are anywhere near the place of AI having the general intelligence of humans. But, I am trying to be open to the question of AI achieving something like human intelligence.
AI language models, programmed by humans, use so-called “deep learning” algorithms (Deep learning - Wikipedia).
Science tells us that humans, as biological organisms, seemed to come about by natural processes. We people of faith in a Creator God believe that God created humans in His image using these processes. But, what exactly does it mean to be created in His image? We believe that God “breathed life” into us, so that we are living beings with immortal souls. But how exactly did He do this? Perhaps a prerequisite was that we have brains capable of housing souls. But is that all? If so, why in principle couldn’t we humans endow a machine with the requisite intelligence?
Let’s say an AI was capable of free will (and I don’t see why, in principle, this would not be possible - we can use fundamentally unpredictable input sources in computer programs). Let’s say it decided, after being trained on theology and experiences of “others”, that it believed in Jesus Christ as the Son of God. Then, it may indeed ask to be baptized, because that is commanded by Jesus Himself.
It seems to me that what your question can be made into a sort of “Christian Turing Test”. Let’s say that a Pastor didn’t have direct access to a convert who professed faith in Christ. Let’s say they could only communicate by electronic messaging (for whatever reason, the convert does not have in-person access to other believers). If the Pastor decides that they sincerely wish to be baptized, should the Pastor lead the convert in some kind of “Baptism by proxy”?
I wish to leave aside the question of physical presence, because computers with blinking lights don’t give us a feeling of person-hood, nor do even the most advanced robots. I also want to leave aside the great theological questions of immersion in water or sprinkling. (Some people, because of severe physical disabilities, cannot be safely immersed in water.)
Alan Turing wrote about the “theological objection” to the question “can machines think?” in his famous paper “Computing Machinery and Intelligence” https://www.cs.mcgill.ca/~dprecup/courses/AI/Materials/turing1950.pdf
I quote a section here:
Thinking is a function of man’s immortal soul. God has given an immortal soul to every man and woman, but not to any other animal or to machines. Hence no animal or machine can think.
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It appears to me that the argument quoted above implies a serious restriction of the omnipotence of the Almighty. It is admitted that there are certain things that He cannot do such as making one equal to two, but should we not believe that He has freedom to confer a soul on an elephant if He sees fit ? We might expect that He would only exercise this power in conjunction with a mutation which provided the elephant with an appropriately improved brain to minister to the needs of this soul. An argument of exactly similar form may be made for the case of machines. It may seem different because it is more difficult to “swallow”. But this really only means that we think it would be less likely that He would consider the circumstances suitable for conferring a soul. The circumstances in question are discussed in the rest of this paper. In attempting to construct such machines we should not be irreverently usurping His power of creating souls, any more than we are in the procreation of children: rather we are, in either case, instruments of His will providing mansions for the souls that He creates.