The question may be wrong in the first point: "I do not want to update every page exchange, as this for playback" , the page continues to run if the HTTP request being made is asynchronous, and as it says in the question, "AJAX" (Asynchronous JavaScript and XML).
The problem is to use AJAX HTTP requests to do chat simulations, games, etc., in which case you might need support on your server to use sockets (or WebSocket ). There are also techniques like Long Polling to minimize the use of your server because of HTTP requests.
So far, as far as I know about some Adsense rules, if the ads on the page are removed, there could be some interference, but that would not be AJAX, perhaps because of navigation that modifies the HTML page.
You can book what belongs to Adsense in containers, and avoid re-generating / modifying these containers while AJAX navigation occurs.