Thanks for the question. Our clients have been using the Tars PPC Chatbots for Google adwords Landing page for quite some time now and they have not seen much change in the Quality Score on their ads.
Quality score depends on many factors including Page Load speed, Bounce rate, Time spend on the page, Content on the page etc…
Most of them actually play a positive role in case of chatbot, because of high load speed, high user engagement etc… We are thinking of also putting in the whole conversation transcript as part of the HTML page itself, so that Google can index it. That will help with the content thing as well.