I just watched the clip (It can be seen here), and there are a couple portions of the scene that lead me to believe that he is in a catatonic state. If you look at Aragorn when he grabs the palantir (at around 1:48-54), you can see him start to faint and his eyes closing. This suggests that the palantir/Sauron have the ability to induce unconsciousness from the mental impact.
Pippin is in a slightly rigid state, and at the cut to him at 2:02ish, you can see his jaw move slightly (Although that may be just the actor). If he were dead, then the muscles would have completely relaxed and he would look less stiff.
As Gandalf puts his hand on his head, the eyes are still open, and I believe what Gandalf is doing is combating the presence of Sauron in the mind of Pippin, and it's the sudden awakening from that presence/catatonia that makes him jump a bit. Also, it's been well documented that sudden, devastating tragedy can induce catatonia/retreating from the world even in healthy, otherwise normal humans so I don't see that as a far stretch. I think the eyes close naturally, I don't think that Gandalf closed them (Unless he did it with his palm :p)