Base on my observation, it seems unlikely. Firstly, the cliff doesn't reach all the way to the bottom so it's not deadly. Secondly, it is quite impossible to take 10,000 unwilling victims up Umm Biyara if you see how steep and narrow some of the paths are. Thirdly, in ancient time, the Hebrew word for thousand could also meant families or tents. It's more likely the king only killed 10 families (40 people?).