Originally Posted by dabac

Don't worry about that. Brake pads needs to be quite sturdy to hold up to the forces generated during braking.
Remember that you can endo a bike by braking too hard. Squeezing a tire past isn't going to worry them structurally.

What it MIGHT do however, is to upset their alignment.
This MIGHT cause the brake pad to gouge the tire sidewall when installed, which can cause all kinds of nasties. Blow outs, brake pad getting snagged leading to endo AND blow out. Pad dropping too low and wedging against rim....