Yes, this is a simple way to think about it: If you choose n uniformly random values in [-1/2, 1/2] (the unit cube) then the sum of squares will be concentrate

Yes, this is a simple way to think about it: If you choose n uniformly random values in [-1/2, 1/2] (the unit cube) then the sum of squares will be concentrated around n/12 (just take the variance). This is way more than 1, which is what you would need to stay inside the unit ball.