No, he did not say he saw Cooper asleep. He also did not say he knew Cooper was asleep.
I believe the context of his saying "he must have fallen asleep" was that RH was trying to explain, and to understand himself, how it was possible he forgot Cooper was in the car. I think he may have said it very early on, as in, the same day or next.
That utterance makes total sense to me, because I think it's the only logical explanation for how it was RH didn't know Cooper was in the car.
One isn't likely to forget one's son is there if one's son is talking or chirping or singing or just kicking at the back seat, for that matter.
I'm well aware that many here don't believe Cooper did fall asleep in the car that morning. From my experience with kids, including my DS and his friends and friend's kids, and (step) grandchildren, etc., I know it's possible for kids that age to fall asleep that quickly in a car, yes, even in the morning.
(Daycare testified Cooper wasn't always awake when RH brought him in, so morning didn't necessarily mean wide awake, and, it isn't necessary to believe Cooper fell asleep in 1 minute, or 2, or in the time to the intersection to believe RH didn't know, only that after RH drove on by the intersection (his forgetting in those few moments a separate event) Cooper was drowsy enough to be silent, and asleep within FIVE MINUTES of leaving CFA, the time it took to reach work.
Subjective, but imo, perfectly plausible. ETA, perhaps all the more so because iirc, folks did walk close enough to RH's car in the AM to be able to hear a wide awake toddler whose father was no where in sight.