My son is now going to a public charter high school after homeschooling all his life. The decision was not the one I preferred, but my son wanted to play high school sports and my husband agreed.
A little background - my son has always been a bit quiet when first meeting people, not extremely outgoing until you get to know him.
He has had no problem socializing with the other kids whatsoever and loves the social life that high school offers. That said, the down side is the behavior and attitudes he's bringing home. I don't know how much of it is just teen hormones, but he seems to have no patience with his younger siblings anymore. How quickly peers can replace the importance of family. I find it very depressing.
That's just my experience. I know it would be different for everyone - some kids do not like the school environment (homeschooled or not) - so it isn't really something you can generalize. There have been studies about homeschoolers that include socialization. You can find some of those at www.hslda.org
Good luck with your project.