Sociopaths, or secondary psychopaths might. They tend to develop emotional suppression as a coping mechanism, either voluntarily or involuntarily. Although the underlying cognitive processes seem to be much more complex than this. Making it very likely that that they will suppress those physical and mental responses before those responses reach any relevant level of affect. It is suggested that secondary psychopaths can go as far as not having any response at all like primary psychopaths, but to my knowledge, the general consensus among researchers is that they still are 'capable' of feeling. Someone who has developed sociopathic tendencies due to voluntary means, will likely say that they are rationally heightened. Someone who was forced to develop sociopathic tendencies might not feel similarly.
The use of the word sociopath is vague these days. For example, my mother is a primary psychopath. When she was young she shoved her brother from a significant height, just because he was bothering her. To this day she doesn't feel 'sad' about doing it. She claims that she 'feels' sad about it, AFTER being through therapy and receiving psychological help. From her family members I learned that her initial accounts of that incident was like 'He deserved it.' 'He was pissing me off.' , she just couldn't process this incident in any other way, nor was she disturbed by the fact that her brother was injured. Her parents always claims that she is just a little bit different and needs more love, that's all :'D . Fortunately she is socially functional and not antisocial at all now and teaches psychology, funny isn't it? She is pretty good at making others think that she is feeling something though, yet it is still hard for her to cry when needed. The most she can do is make a facial expression that resembles sadness - which implies that she cognitively knows what sadness is.