Doesn't seem to bother the squirrels in my 'hood, as I've been using a Havahart trap open on one end to trap chipmunks, which can do huge damage as well, only from a different angle - they tunnel under your driveway, garage floor and/or foundation and undermine it - next thing you know your driveway's 6" lower than you garage slab! Anyway, I've had plenty of squirrels in that trap and like I said it's only open on one end.....
Don't bother to trap or kill all of them, for every one you do 10 more will move in due to the lack of competition! You may make a temporary dent, but they'll be back......
The only thing you can do is trap and kill the ones that have gotten in, then figure out how/where they did and fix it so they can't get in again. Sometimes just getting rid of the "problem child" does the trick, as not all of them are predisposed to getting into the house. Do the usual safeguards (trim back the trees and such) but in my house they climb right up the chimney.
On my house they tore off cedar roof shingles over a dormer and tore thru the soffets too. I put metal flashing under the shingles and alll along under the soffits when I rebuilt the damage, so if they started scratching on the wood they'd hit the metal - so far so good.
Good luck!