Seemed to me he did. It happened fast, but I think I saw him jump off the horse, point his Colt Walker at the horse's chest and fire; the horse immediately fell and Gus laid down behind his carcass, using it as a barrier. The country they were in was a flat, arid, level desert with no natural cover anywhere in sight. There was a little depression in the ground which Gus picked as the place he'd face his pursuers, so downed his horse there.
That's one of the things about "Lonesome Dove"- they told the story without many of the usual restrains. Two kids get killed by a renegade names "Blue Duck", one of the central characters gets hanged after he fell in with some evil guys who killed and burned a farmer and his son...
By the way, Blue train is right, "Death Hunt" was an excellent gun movie. The continuity people did a good job of getting things right. It's one of Charles Bronson's most convincing roles. As for accurate history...well, it made a good story anyway, and Bronson gets away at the end because the leader of the pursuing Mounties (Lee Marvin), lets him go, which was reasonable given what had gone on in the movie up to then.