No, according to all independent medical and court-appointed observers; she displays involuntary muscle and body reactions. IOW, this happens frequently, whether her mother comes into the room or not, whether she is facing her mother or not. The same goes with her waking up and moving or making noises or sounds. All noncognitive.
Why do you think all her family has done is show tiny snippets of videotapes? Because they allegedly show congitive ability. Haven't you ever wondered why all 11 court cases were won by Michael after the court-appointed observers spent time examining Terri DESPITE initially observing the video snippets from Terri's parents?
Because reality doesn't support the parents' claim of cognitive ability. Not even their lawyer's recent fantastic claim that Terri yelled she doesn't want to die - even Terri's own family was surprised at that one (according to them all she did was make noises).
We know this... how? After all, we know that 120,000 people die every year from the infallibility of doctors. We have at least one Freeper who is supposed to be a vegetable (according to the doctors who examined) with no hope of recovery. I'd say that Freeper's typed comments show at least some degree cognitive ability, yes? For every 'expert' there is one who will contradict. That is why they are called medical opinions, not medical facts.
Does Terri have any power of reason, or really any chance of regaining it? No. That is not in dispute. Could she have some quality of life with proper therapy? Maybe. But what is really in dispute here is whether she would wish to commit suicide if faced with that choice. All we have is the word of her husband, that many would consider suspect, that she would. What we are saying is that is not enough. She is not his property. What possibly could be the harm of divorcing her and allowing her parents taking over her care? Those questions have not been answered to any degree of satisfaction, by any court ruling.
Lastly, Mike Schiavo took up with his current girlfriend 6 or 7 years ago but there were others before her. Evidently, he doesn't consider his vows to be binding when they become inconvienient. It isn't admissible in the court of law, but it is in the court of public opinion.