I decided to watch the episode where Ash catches his Roggenrola, my logic being that he had to make it faints before throwing the Pokeball.
Roggenrola faced Tepig. Tepig finished off the fight with Tackle & Roggenrola went flying. He was down, but he was still moving, so he did not faint. He was just knocked down, most likely weary from the battle. Then Ash threw the Pokeball, all the while Roggenrola was on the ground but moving his feet, and caught him.
So he did not faint in this episode.
Then the battle he had with Clay. He did not faint, but instead evolved. I don't think he does faint in the show. I'll keep looking.