Kate,
The letter that you reference certainly sounds authentic. Normally there would be other records extant to verify his service, but it looks like they do not exist. However, one other thing to note is that the lack of early records for this regiment is documented. The first regimental return on record for the 24th Mississippi covers the period Mar. Apr. May and Jun 1862, and is dated 22 Jul 1862, Tupelo M&O (Mobile & Ohio) RR. It states: "Companies Books and Papers have nearly all been destroyed Mostly by order. A great many important Regimental Papers and Books were lost in the evacuation of Corinth, Miss. Thus a complete history of the Regiment - Changes of Station, precise duties &c cannot be given."
In my opinion, for what it's worth, this gives more, not less, weight to the document stating the acceptance of his resignation. It does not state whether he was a staff or line officer, but the evidence it gives for his service in the 24th Mississippi is strong.