Since no one has responded yet I'll provide a couple of thoughts. I'm no expert but had ancestors in the MSG and later in the CSA.

My understanding is that there was no automatic transfer but that as MSG units ended their service they were encouraged to enlist in CSA units.

Several of my ancestors served their first 6 months in the 1st Infantry Regiment (Wingo's) of the 7th Division (McBride's) of the Missouri State Guard. As their enlistments expired in late 1861 and early 1862 many went home but some reinlisted in either MSG or CSA units. William O Coleman, who had been the adjutant of Wingo's Regiment, was given the assignment in January 1862 of raising a Cavalry Regiment which was originally designated the 4th Cavalry Regiment of the 7th Division MSG. Coleman's commision as a CSA Colonel occured that summer. Coleman was directed to return from MO to AR but he refused and was fired and his troops became part of the origins of the 10th Missouri Infantry Regiment. It's not clear to me if those men that joined in the 1st half of 1862 (before Coleman's CSA commision) considered themselves as MSG, CSA or both. Those of Coleman's command, like my g-g-grandfather, that were captured during that time were generally regarded by the federals as "bushwhackers".

Also, my understanding is that there were MSG units fighting at Pea Ridge and that crossed the Mississipi with Price and Van Dorn.

I don't know if this helps but I thought it might stimulate some other discussion.