Can a sociopath actually feel bad about him/herself and want to be like other "normal" people?
No. Because a sociopath already feels 'normal' being just the way they are. Well, I can't really speak for other sociopaths. That's how I feel anyway.
Feeling 'bad' requires a moral conscience and that is something that most (if not all) sociopaths do not have have.
Also, the way I see it, most non-sociopaths rely too much on their emotion, which can make them irrational at times. It also makes them easier to manipulate and exploit. Why would I want to be like that?
Don't be disrespectful for the schizoids, tho...
If a sociopath is aware of his condition, then he might start wondering what's it like on the other side, especially on the moments of failures. Such wonders might lead to feeling bad about their condition, especially since it would mean blaming something aside themselves (a condition).
I have a cousin who is schizoid... Super cool dude. works a job at a Disney restaurant doing dishes. Thrill is a lazy fuck that somehow has convinced herself she's a badass sociopath. We all know she's too worthless to be anything other than an oxygen thief.