I don't think I've ever seen this topic brought up before...kudos! I thought I had seen it all.
Personally, I think if it had been Giles and Dawn up there, he would have apologized, and then let her die. And Dawn would have agreed. Remember that Dawn tried to jump but Buffy wouldn't let her. Giles would have is the difference.
But it's all a moot point because Spike, who was also there, would have never let Dawn jump, or die for that matter. He promised to protect her until the end of the world. It it had been a showdown between Giles, Spike, and Dawn (say the Doctor has already left after cutting Dawn) Spike and Giles would have had to throw down, because Spike would rather kill or be killed then let anything happen to Dawn. He'd rather the world end.
So, are you asking if Giles would let Dawn die? Absolutely. No doubt. We've seen that Giles is capable of making the hard decisions, hence Ben/Glory.
What would Buffy had done if she had been too late and Giles had let Dawn die?