I've used my 1D X with a 600/4 II and 2xIII to track birds in flight, sometimes handheld. It does fine. However, when shooting small birds in thickets (branches in front of and behind subject), where the bare 600 II locks onto the bird easily, with the 2x it hunts a bit - in that situation, it behaves a lot like the bare 100-400L.
Did you use spot single point or regular single point focus for this test?
Thanks, Will T.