Worked as a scientist at a German university in AI, especially in Natural Language Processing, for the last 7 years. Answering simple questions like during this registration process (at least as I remember them) should be no problem.
https://en.wikipedia.org/wiki/IBM_Watson
Watson won Jeoparty over a decade ago. There was a lot of hardware and engineering needed for this project. With todays transformer based methods and pre-trained models you can do this with a consumer pc that has a mediocre gpu installed. In fact, Question Answering is one of the main tasks on which the NLP community evaluates the developed systems.
I know next to nothing about AI, but if the technology is good enough to thwart anti-spam tactics, surely it could be used to identify spam posts and delete them, is there a service out there that could be used?
Algorithmically, there is no difference to your spam filter in your mail client. The question is: does the software in the background of this forum have an API that connects with a good spam filter? I could imagine that there is already something like a spam filter in there that just hast to get configured or if it's some commercial software that there is a module you can activate/install for money.
A good system also would learn from the mistakes it made: If there is a spam post that dropped through the filter, the moderators should not only be able to delete it, but to mark it as spam, so the filter can update its internal model with new examples. Just as every good mail client out there works.
Unfortunately I'm no expert for forum software. Hosted a forum for my band many years ago, before messengers were a thing (I would prefer the forum 'til today). But since there was no public registration possibility I had no such problems.