Aborting an HTTP request. Server-side advantage?

In, for example, JavaScript AJAX libraries it is possible to abort an AJAX request. Is there any server side advantage to this or is it just for client-side cleanliness? Is it part of TCP?

If, for example, I am requesting via AJAX a Python based server service – which is resource intensive – from my JavaScript Web App and abort this AJAX request, is it possible that aborting will ease the load on the server, or will the my ajax library just ignore the response from the server?