No. Sociopaths by definition have underdeveloped superegos or more simply, no conscience. They do not know the difference between right & wrong, have no moral code of ethics and therefore do not feel shameful when they have done something wrong.
Shame. Very important question to me. I think most research is not accurate because it does not encompass or deal with the phenomena of shame. And i mean by this the thomkins/ nathanson definition. Nathanson's book "shame ; pride " deals with this question elegantly in a few pages. He ; i believe they feel shame ;what you see in an adult psychopath is the consequence of shame trauma in early life.
Shame. Typically not. For the most part, sociopaths, more properly known as those with antisocial personality disorder have no appreciable sense of right and wrong. They have no conscience for the most part, and therefor largely are incapable of feeling shame.