My understanding is that people can develop social processing skills by consciously practicing unnatural habits until they become natural.

This is correct; at least some people can do this. For someone reason, there is a cultural bias that makes believe that this approach doesn't work, because so many people seem to believe that it doesn't without evidence. These people are wrong; this view has already been falsified by many people.

Many people learn many different disciplines through the four stages of competence (unconscious incompetence, conscious incompetence, conscious competence, unconscious competence), in sports and the arts.

Conversation isn't a special exception. Though it may be different from those domains by requiring more specialized mental hardware. Consciously practicing "unnatural" social habits happens to be a good way to jump start that hardware if it is dormant.

Someone without this hardware may not be able to learn how to emulate naturally social people through consciously trying to emulate them. Yet I bet that most people with social difficulties short of Asperger's aren't missing the relevant hardware; they just don't know how to use it out of social inexperience, such as from spending their formative years being isolated and bullied for being slightly different.