I'm hoping so! The "normal social interaction with peers" that my DD13 had before we pulled her out of school was kids calling her "weird," along with other names, making fun of her, and setting her up to get in trouble (strangely enough, no one but my DD ever got in trouble, though). At 8 years old, my DD was wishing that she would "fall out of a window and land on a sword and die." She was suicidal until a few months after we pulled her out of school when she was 10 1/2. No one even told her good-bye on her last day of school. Great social interaction...just what every good parent wants for their child.
Now that she's homeschooling, she's a much happier girl. She takes a sewing class with other homeschoolers, as well as a writing class, both of which meet weekly. She was taking a PE class for homeschoolers, but we quit last year when she broke her wrist and couldn't participate. She is also in dance class/rehearsal 4-5 days a week. She loves to go to the mall with her friends she's made at dance class, and to have sleepovers or lunch dates with them, too. I don't think social interaction is a problem.