I have had invites while in a game before, so if you don't catch the little pop up in the top left corner, then you can still do something and that is to hit your escape key, or click the three dot menu at the top left corner of the game window, to open the left pane. In that pane you should see an invitation button, but it is only there for two minutes...
...so you have to be fairly quick to catch it. Clicking the invite gives you the option to accept or decline joining the game.
That chart on the previous page was for the old flash game and as far as I am aware, we can't turn invite notification sounds off. You could turn the master volume off in settings, but then you wouldn't hear anything at all.