Does it matter what ISO you use on a camera, if you have an external mic?

I just got a canon 7d and people tell me you shouldn't change the ISO above 640 because then it would cause background noise to be high. So my question is, if I use a boom mic will it matter what ISO I put it on, I need a high ISO for shooting at night, so if I change the ISO to lets say 1600, will the background noise show up if I have a boom mic?