Actually, it's entirely possible. My son's in college now but when we were homeschooling, we knew a few highly gifted kids and they truly are self-driven, hard charging type-A personalities. One family started their daughter out in public school, but after a while, she would hide in the closet and cry every morning and beg her mother to let her stay home. She was bored in the extreme (in the ludicrous, socialist world of public school the teacher wouldn't allow her to read books when she finished assignments early because it might make her classmates feel bad). The other kids didn't like her because she was smart (she wasn't like THEM) and teased her constantly.
Finally her parents decided to homeschool her when she was about 9 and both parents and daughter felt like a great weight had been lifted. She finished correspondence high school in a year (and probably would've done it sooner but mom put the brakes on and made her do other activities as well). She played classical piano beautifully and even gave lessons to other homeschoolers. She also loved biology and writing plays. I don't ever remember thinking she was arrogant (though she wasn't afraid to give an answer if she knew it) and she had plenty of friends, including my son, who's a pretty regular guy. But because her mind went a mile a minute, she would finish up one project and immediately be ready to start the next one. Her parents toughest challenge was just trying to make sure she had enough to do.
Also, while it's not exactly the same, my son was a gifted soccer player (classic at 9, adult leagues at 13, training in Europe at 16). Before I had him, I'd hear about some figure skater or gymnast and her grueling schedule and wonder how her parents could DO that to her...I was NEVER going to be like that...it bordered on abuse. Sometimes God has interesting ways of showing you how little you know.
This boy, from the time he was 4 would eat sleep and breath soccer...he slept with a soccer ball instead of a teddy bear. I'm about as athletic as celery, so this was like living with a foreigner. He played year round, indoor and out, attended every camp he could find and thought it was cruel and unusual punishment when we did make him slow down. Twice he was injured badly enough that he couldn't play for a while and he was an absolute bear to live with. At no time did we force him to play, to tell him what team to try out for, etc. In fact, his drive made me tired. He hated how cut-throat and competitive it was, but he loved the game and you could see it in his entire body when he was on the field. When he started college, he just decided not to play competitively anymore (good thing since his school doesn't have a soccer team). However, I learned a good lesson about not prejudging families whose kids and parents seemed "too" involved in one activity or another.
Cindie