No. Enabling the third click will delay the animation after the second click, eg the app switcher, but not the close app animation.Sure it should. It has to wait to see IF there are going to be more presses before it reacts. So waiting for a 2nd or 3rd click before responding.
There will always be a delay after the first click, it waits for a potential double click. That delay won't change by enabling the accessibility option (triple click).
Think about it for a while...