Rumple and Regina had a discussion about Rumple being the one to ‘procure’ Henry for her.
They didn’t say anything about getting him from someone ‘on the outside’.
Knowing Gold/Rumple was involved in the adoption in some way, I would think that August wasn’t. I don’t think they would have had any contact with each other until AWB posed as Bae because Rumple was almost totally convinced that August was Bae – if they had contact before then, Rumple would have recognized him.
Plus, it was made clear that August was in Phuket when Emma found out that she was pregnant, and he was still there 10 yrs later when She arrived in SB.