Having no experience on this type or indeed any FBW aircraft I have no idea of the relative "feel" of the controls A/P engaged or disengaged.
Given the situation they found themselves in , I don't find it too surprising that they could have missed this, assuming the control feel is similar.
On something like a B737 it would be fairly self evident , as the controls (even in CWS) do not feel the same, and anyhow the aircraft would have wandered off on a tangent, but with FBW, gust alleviation, and all these other boxes of tricks between you & the hardware ? perhaps someone experienced on type can tell us.
Well if you for some reason are trying to manhandle the controls on a triple with the A/P in you'd certainly notice, in the same way as if you tried to manhandle a 747 with the A/P in ( the 777 I fly doesn't have CWS, is it even an opton?). In my experience you only really notice the fact that the 777 is FBW if you get close to the edge of the envelope ( in the sim I hasten to add), when the various protection features start to kick in. Otherwise it behaves and feels like a conventional aircraft...then again of course it does, it's a Boeing
