I have never known them to get caught in the netting. Their eyesight is pretty good (except for that solitary bird that flew into our kitchen window), and it's not a trap like fishing nets. It's basically just barrier protection.
But bear in mind that netting won't stop wasps, ants, etc, whereas the organza bags will.
Urban pigeons might be edible but for the accumulation of lead in their bodies and the not insignificant risk of contracting Chlamydia from them.