Blocking ajax can be done at server side. Depends on the technology you are using but let the ajax call a page on your website and just put a thread.sleep or similar...
To really simulate this, you'll have to get the configurations of the server, and know exactly what types of calls are being blocked.
In a lower level, ajax calls are made much like normal requests. So you may be able to get around this by settings custom headers to simulate allowed requests.
They probably won't give you this information, but if they do, it will be easy to check in your server-side the presence of the header, and return same status if it's not.
Without details of the server config, I can't help you more than this.