I just wanted to agree with Lorel's post. We are new to homeschooling this academic year, and my son leans extroverted. I think he gets more positive social experiences than he was getting at public school (where he seemed to seek out the kids that were goofing off).
He plays with kids outside our house almost daily. That being said, we do live in an urban area with homeschoolers of all backgrounds (I know some areas have predominantly religious homeschoolers) and specifically have found a GT home school co-op. Although I do think co-ops can work well, even if they are not GT specific. If homeschooling is something on your radar (even if it might be some point in the future), I would put feelers out for opportunities in your area.
