AJAX is just a typical HTTP request. Imagine you have 10 000 requests per second. You know your server, it possibilities and your numbers, do a simple math yourself, only you may answer your question, but in general, of course, more requests will affect a performance somehow.
You may do old-school AJAX request every 10-30 sec to check for updates or you may use today web sockets.
If server will have performance issues in the future then you just will set up proxy, load balancers, implement caching in both client-side and server-side. It is absolutely normal situation.