Yes, the National Archives lists the unit for him as you mention. It also states look at the 4th Battalion Mississippi Cavalry records. I did, and a John A. Chappell, private, served in Sykes Company of the 4th MS Battalion. Both units were part of the 2nd Regiment of MS & AL Cavalry. With attrition of the ranks, it was not uncommon for soldiers of one state to come under command of units of another state.
I then looked at civilwardata.com, and they show the same info, ie, JAC listed under both units. Unfortunately, they show nothing about capture or POW data for the man.