The exact number of officers is known but that of enlisted men is considerably less so. The best estimate I have ever seen is less than 200 enlisted men deserted to join the CS and to my knowledge none who did gained any prominance by doing so. Wheras many a Corporal or Sgt in the regular army was offered a commision in a Volunteer Regiments. It is a very difficult question to answer with any certainty as an enlisted man could not resign but would have to desert. Several enlisted men who deserted prior to their surrender did make it back to the US and had been listed as deserters but that was corrected. Some of the enlisted men who were made POW's early in the war, particularly in Texas, were made an offer to jopin the CS forces but to my knowledge none did so. Part of that was a general sense of betrayal by people they had been working to defend and added to that many of those who were surrendered were then robbed of all monies and valuables by their captors while some of their former officers merely looked on. Not something likely to endear men to the CS.
The pre war US Regular Army was a tight knit group and many a soldier and NCO knew each other rather well. By and large, from what I've read, those regulars were anything but friendly toward the CS. At least some of the issues of reconstruction was pre-war regulars with a grudge against the south in general.
That Body of Brave Men by Johnson goes into some detail on the subject but I cannot recall how much.