Most use neurotoxins. That's what all those chems are. So yeah, they are paralyzed in a way... they get fried and all systems shut down.
I use all all-natural, non-poisonous brand that smells like strong mint. It's like blasting them with an altoid.
Smashing them has its gratifications, especially if you have had a bad day. I live in FL where the roaches fly at night...