If you happen to have Randal Munroe's what if? [1] on your bookshelf, look up the chapter titled "Sparta". It should convince you that the story of arrows blocking the sun is probably not true.
If you don't have it, you could try to do the math yourself. Munroe assumes that 1) an arrow intercepts 40 cm² of sunlight, 2) an archer looses 8 to 10 arrows a minute and 3) each arrow spends an average of three seconds in flight. You could adjust those numbers to taste, but I would not expect the conclusion to change.
I don't have time to find a link now but if you google it you'll see.
(Incidentally, it's also in the movie 300)