Would noise really be an issue with zombies though? They attack anything that moves that's not one of them, and can smell even the faintest hint of non-coagulated blood even if you barely nick yourself on an exposed nail, and in some respects are hypersensitive to changes in light like from a flashlight.
Personally I also think it'd be useless if you get surrounded should you step on loose gravel or some broken glass or whatever, because even the fastest Archers can't put out one hundred arrows in the span of 20 seconds that it would take for the zombies to close in and suck your brain out of your cranial cavity like a frapuccino...
=P
Yes noise would be an issue. With a pistol or rifle each shot would be heard by every zombie withing sound range who would come investigate the sound. A bow weapon would not draw their attention.
As to the second part where I made a stupid mistake and found myself surrounded I wouldn't even attempt to try to fight them all off with my bow. I would pull out my melee weapon or use another tool. (unless for some reason this is all set up in a hypothetical situation where I was stupid enough to find myself out fighting zombies with only a missile weapon. which wouldn't happen)
Try reading the zombie survival guide it gives a detailed list of weapons and why and why not they'd be useful against the walking undead.
so what does it say on the matter?