Not really, no. The whole thing is heavily fictionalized in the film.
The killing of his son is fiction - in fact, Glass having a son is fiction - at least a son who got killed in front of his father like that. Historical Hugh Glass was *just* left behind by those two men and he sought revenge for being abandoned, but in the end, didn't kill any of them, though he tracked them down.
As far as his actual ordeal goes, he basically dragged and limped and rifted down the river for a couple of hundred kilometers to Fort Kiowa. In the film he is shown as having superhuman rejuvenation abilities, with his broken leg healing itself in a very short period of time, him running and swimming and and riding and fighting and being seemingly unaffected by all the wounds of the bear attack and so on and so on.
I mean, I'm all for artistic liberties and I'm not saying that the movie is bad because of this or that seeing a two-hour-long film of showing a man dragging on the ground would be entertaining or particularly thought-provoking, but some of the stuff shown in the film really broke the (again that word) immersion for me. I was just staring at the screen at several moments thinking "Well, that's just impossible."