It seems to me that you are asking if a child of 3-years-old must socialize? The questions following that might be: What would happen if they did not socialize? Are there negative repercussions? For a child who is struggling with socialization skills, is introverted, has no desire to socialize, then do the negative interactions of forced socialization result in negative repercussions?
I am not sure there are studies that hone in on that specific question, as the assumption seems to be that humans must socialize; Therefore we must teach our young children to socialize. This way they can develop the skills necessary to socialize appropriately as adults. The question then becomes, if we do not force our young (3-year-old) child to socialize, will s/he have the opportunity to develop these skills later on in life or will s/he fall behind with an ever widening gap that is difficult to fill? It has been found that early intervention on many skills for children with ASD results in the development of those skills at a better rate than children with ASD who don't receive those interventions until later (I don't have a reference, sorry). It would seem to be a natural assumption that early intervention for social skills would work the same way. However, I can see the concern if the child is having negative interactions repeatedly and only learning to dislike/fear socialization and further hindering future positive social interactions. So, it would seem to me if a parent wants to provide early intervention for social skills learning, care must be taken to keep/make those interactions positive and useful to learning skills.
This article is not a direct answer to the question, but has some interesting information about how to help young children socialize through positive interactions in parent play with examples.
http://humsci.auburn.edu/parent/socialskills.html