Of course he can pull him up. Its a heavy lift, but far from impossible. I even think Bale would be able to do it for real in the shape he was in back then. No problem. With adrenalin pumping the human being can do extraordinary things.
Even if he couldn't do it, its a film. Should we compare everything we watch in films to real life? That would take time, especially in the Sci-Fi, Horror, Action, Superhero and Disaster genres. Almost every film ever made distort the real world, why shouldn't they.
Look at the muscle mass this man put on for the role. Incredible. Of course he pulled Liam up. Im sure it was bloody difficult but not impossible. Im sure a little movie magic was used...I wouldnt believe he pulled him up off a cliff.
Wait, are we talking about the wide shot of "Bruce" pulling up "Ducard", because if we are, I'm pretty sure those were the stunt doubles for them. Buster Reeves and Mark Mottram were their respective stunt doubles. And when they show that shot of Christian up close pulling up Ducard, if you look closely, you can see that it's not Liam, it's his stunt double. Also, I just saw Liam on some show mentioning that he doesn't do his own stunts.
Yep it was stuntmen who did the slide, but the closeup of Bale pulling Liam up, was Bale, but it was staged some place els, and of course he was not freely hanging from the cliff. Anwyay it doesn't matter who it was, the question is: Did it appear credible that Bale could infact pull a grown man in one arm, and yes I think it is possible.
It looked like a dummy from the top view, and the side angle looked like stunt men (not really Bale and Neeson, just two really bad stunt doubles). I'm not sure if Bale really did that, but I my be mistaken. I'll watch the scene again and study it later. This has got me thinking...
In the special features on the 2 disc the ledge scene was filmed with the stuntmen Buster Reeves (Bale's) and Mark Mottram (Neeson's) as for closeups those are done with dolley cames which mean the cords hold up the real actors while the cam focuses on their expressions
while the far shot consists of the stuntmen doing their thing.
To answer the question, no Bale did not lift up Neeson because that scene was done by the stuntmen. You only saw Bale's grimace pulling up Neeson's stuntman who was already hooked on a line.
However Bale was strong enough to actually carry the taller Neeson which was pretty impressive considering the weight he had to put on his back while standing up straight. Essentially a fireman's carry for 30 feet.