A card in each of the records of 17 privates of Brown's Battery - John L. Allen, William Brinkley, George W. Campbell, J.W. Canard, Philip Canard, Joseph Cummings, Sol N. Freeze, Henry Green, Joseph Haynes, James A. Hitchcock, Sebert Martin, R.M. Mays, John Odle, John Plumlee, Benjamin Roper, R.M. Stevens and Richard L. Ward - shows them as being present with Shaler’s Regiment in March/April 1863 (although Ward was absent sick) and that they had been transferred to the regiment as per SO. 23. Six of the other privates had been discharged from the service on 13 March 1863.
I think one thing still needs to be borne in mind. The CWSS lists only 34 names against Brown’s Battery. This doesn’t come anywhere near the 120 men requested from McBride‘s Brigade to be assigned to the battery. Even if most of the members of the 27th Arkansas were ordered to return to their commands under SO.23, there may still have been enough men left to man the battery and keep it going. Personally, I believe that, due to the potential loss of materiel that you point out, the battery was disbanded in April/May 1863 but I cannot be sure. We would probably need to identify men from other regiments who were transferred to Brown's Battery and see what happened to them but, from available sources, I think that would be difficult.