Nope. They release an egg "capsule"Probably the reason I have billions now...
While there is a good chance you might smash that, as long as you clean up all the mess the eggs are gone.
As a kid in Durban, growing up, my mom use to use cockroach blocks.
Roaches eat it and die, also seem to recall it renders eggs infertile.
Someone recently mentioned they still sell them.
Tried finding them in joburg. No luck so far.