Using PythonAnywhere as a game server
Yes, client code can talk to your project at PythonAnywhere, as you will be given a unique project url like http://yourblogname.pythonanywhere.com/. Your server will listen the 80 port at that url.
It depends what sort of connection your clients need to make to the server. PythonAnywhere supports WSGI, which means "normal" HTTP request/response interactions -- GET, POST, etc. That works well for "traditional" web pages or web apps.
If your client side needs dynamic, two-way connections using non-HTTP protocols, using raw sockets, or even websockets, PythonAnyhwere doesn't support that at present.