Iverson "Ive" Batchelor was 16 or 17 in 1862. I have many in the PCA who were 16 and even a few younger. At 16 you had to have parent's permission and some had that. I have on record one who's father yanked his 16 year old son out of service only to have him join back up at 17. I have at least one case of 16 year old son with father joining up and fighting side by side for years.
Batchelor's young age probably explains why there is no record of him in the CS service until 1864 (although he was apparently in the PCA at 16 in 1862).
The Albert Batchelor files you mentioned show "1863-1864, letter of Iverson G. attending school in Liberty, Amite County expressing concern over the situation in Pointe Coupee Parish ..."
By 1865 we find ..."letter of Iverson, near Liberty, Mississippi with his regiment giving war news". At that time he was in the 2nd La. Cav.

You know, the PCA may have ordered young Ive to stay there and watch their stuff and make sure the men of the 1st Ala. didn't rummage through it. You never know.