Of course it could. The more interesting question is how it will be acknowledged, by mathematicians, by the AI interests, and by the media.
As with many other fields, computers offer the opportunity to search vast mathematical spaces that are beyond the ability of humans to investigate.
But the as yet unanswered question is how to tell a computer to look for something "interesting". In searches for drugs, for example, we might ask the computer to find a drug that will bind to a particular site or otherwise disrupt a metabolic pathway, but ask it to find *new* interesting ideas is beyond description, let alone execution.
This isn't particularly surprising, it's a vanishingly rare skill even amongst humans skilled in the field.
And so it will be with AI proofs. There will be great fanfare the first time an AI proves, with or without guidance from top mathematicians, some previously unsolved conjecture. "ChatGPT proves the Goldbach Conjecture! AI surpasses human intelligence!" but assuming that the Goldbach conjecture can be proved using already known mathematics then all the work is done, and all that remains is searching, something that AI is particularly good at. The search space is vast however, and it's just as likely that the only way an AI can find a proof is with the intuition of genius mathematicians stopping it going off down unproductive routes. The AI will find the proof but it may, or may not be something it could have done alone.
And, should it happen, it's quite likely that the AI proof will spur countless interesting discoveries by the mathematicians skilled in the field once they see the "trick" to solving that problem. Possibly half a dozen other unsolved problems might fall, not due to AI but due to *understanding*.
The second thing that will happen, but probably will slip most of us by because it won't make the mainstream press and we don't read mathematics journals, is some deep and profound new conjectures (with or without proof) that will be mostly the work of mathematicians but with a good dose of AI assist. This may, or may not, get credited to AI but will involve the sort of intelligent searching that AI can deliver on a scale that isn't possible by humans due to the limited number of them, their low speed relative to computers, and their propensity to make mistakes, particularly when doing boring grunt work.
The final thing that probably will happen eventually but doesn't appear to be on the horizon, is AIs coming up with new and profound conjectures absent the guidance of mathematicians. This is going to be hard to identify, not least because there's a vast difference between a computer coming up with 200 "conjectures", 198 of which are "completely wrong headed", 1 of which is already known and 1 of which the mathematicians looking at its output say "Ohhh, that's interesting" and an AI coming up with 3 conjectures, 2 of which are already known/proved and one is new, novel and interesting.