uh... yes, yes it is. see for example http://mathworld.wolfram.com/HyperspherePointPicking.html
Edit: yeah oops, I goofed and I'm wrong. I didn't notice it was randn - normally distributed. No culling necessary.
Or do you mean more that it sucks pretty bad to generate 300 rands and then throw them away, even once?
You are going to choose 300 random numbers between -1 and 1, and then throw away this batch if their norm is greater than 1. As you increase dimension (in this case 300), you are including more numbers that give a non-negative contribution to this norm, and so you are increasing your chance of rejection with each dimension.
Re-reading your comment, I notice you made a higher-level note regarding the volume of the hypercube vs. hypersphere. While my comment was right, I now think you are right that the volume ratio of hyper sphere to hypercube is, in fact, always over 0.5. I'm gonna run a quick simulation anyway, but you can convince yourself of this by considering that the line segment connecting (1,0) and (0,1) in 2D lies within the unit circle, but a similar construction will always work for high dimensions (I think).
Jeez, my intuition stinks. I initially thought it was obvious why the 3D sphere to unit cube ratio is > 0.5, by analogy to the 2d diamond embedded in a square, but in 3D the embedded octagon volume isn't 0.5. Obvious now, but that'll teach me not to guess.
Indeed, rejection sampling the 300 dimensional unit sphere will suck really bad.