Did Vader/Anakin use the Force to kill Palpatine?

Question

  Moments before he overthrew Emperor, Vader was badly beaten by his own son, Luke Skywalker. He lost his hand, and was described as being weaker than ever before. Yet, he somehow managed to rise, and after brief pause grabbed and carried Palpatine, for a few seconds enduring full strength of Force Lightning by arguably most powerful being in the Galaxy. Some people even compare him carrying Palpatine to Jesus carrying his cross. Both sacrificed themselves with great pain, to save the world.

  Anyway, Anakin Skywalker was Choosen One of the Force, shatterpoint of Palpatine, and absolute shatterpoint of Sith. Yet question is, in his final act, did he use the Force, or better did Force help him to endure what others could not ? Because, even Yoda deflected Palpatine's lightning to survive and did not sacrifice himself by soaking it. If Anakin did not use the Force, then whole scene gets even greater symbolic meaning - heroic act of single individual against whole darkness of the universe.

Answer 1

It wasn't the Force. It was sheer will.

Vader summoned his own will to defeat the Emperor, as described in the official Return of the Jedi novelization by James Kahn and George Lucas. Here is the relevant passage from the climactic scene:

At that instant, Vader sprang up and grabbed the Emperor from behind, pinning Palpatine's upper arms to his torso. Weaker than he'd ever been, Vader had lain still these last few minutes, focusing every fiber of his being on this one, concentrated act — the only action possible; his last, if he failed. Ignoring pain, ignoring his shame and his weakness, ignoring the bone-crushing noise in his head, he focused solely and sightlessly on his will — his will to defeat the evil embodied in the Emperor....

He held the wailing despot high above his head, and with a final spasm of strength, hurled him into the abyss.

(Source)

Therefore, as you say, this was indeed a heroic act by a single individual rallying against the darkness.

Answer 2

Probably not

As @Praxis explained in his answer, the Episode VI novelization does not give any indication that Vader used the Force. Similarly, the Episode VI script does not mention any use of the Force on Vader's part:

Vader grabs the Emperor from behind, fighting for control of the robed figure despite the Dark Lord's weakened body and gravely weakened arm. The Emperor struggles in his embrace, his bolt-shooting hands now lifted high, away from Luke. Now the white lightning arcs back to strike at Vader. He stumbles with his load as the sparks rain off his helmet and flow down over his black cape. He holds his evil master high over his head and walks to the edge of the abyss at the central core of the throne room. With one final burst of his once awesome strength, Darth Vader hurls the Emperor's body into the bottomless shaft.

The script does mention the use of the Force in other contexts. For example, just earlier in the script it says that Luke attempted to use the Force to deflect Palpatine's Force Lightning:

Blinding bolts of energy, evil lightning, shoot from the Emperor's hands at Luke. Even in his surprise, the young Jedi tries to use the Force to deflect them.

The fact that there is no mention of Vader using the Force when he killed Palpatine therefore suggests that Vader did not use the Force -- only what remained of his own strength.