Abort the connection only stops the download of that file to your HDD, browse cache, etc. and doesn't terminate your internet connection.
There is no need to delete a virus that isn't yet on your system, the Web Shield pre scans content before it is saved to your browser cache, prevention is better than cure.
I would have thought the X would be no action Abort or otherwise, but the Standard Shield may provide back-up if it is saved to the browser cache. I would suggest that you clear the browser cache and do an avast on-demand scan.