I voted "Yes, but allow one official bot that seeds replies in a special section" because complete banning might be difficult. This is probably inescapable now, so a limited sandbox area may allow us to understand how to deal with them better.
Consider these situations:
1. An unscrupulous person posts a question. On the surface it could be either seemingly legitimate or obviously trolling. The conversation proceeds until the reaction they were looking for is achieved, which wastes time for others.
2. An inexperienced person posts an answer to a question that required looking up something for which they had no knowledge. Perhaps information from another web site is copied over as the answer. A few cycles go by and they become unable to proceed, wasting time and making the situation confused. Would this be considered a case of something similar to plagiarism? Trolling?
One of the problems with AI is that it could take on either of those roles, likely for malignant purposes because they aren't self-driven yet: they require someone to direct the original question to it. Imagine a situation where someone makes a program to a forum for questions, submit them to an AI, and then post the response to the forum using automated means. Would 3 per day be a problem? 10? 30? 100? How much would it take to submit the question to an AI with a modifier such that the answer is slightly wrong? How much of the trust and legitimacy of the forum relies on reasonably correct answers? A malignant AI could, over time, contaminate the system enough so that everyone else loses trust in it.