Would cockroaches eat eachother to survive?

Over breakfast we were discussing ways of detecting nuclear leakage in a storage facility. I put forth the idea of genetically modifying cockroaches to turn a different color upon exposure since they are among the only things to survive radiation. But then someone said that might not work well because the other roaches would just eat their counterpart.

Apart from being disgusting, could a cockroach eat one of their own to get along (considering mouth size, shell, etc…)? Would they?

Absolutely. Cockroaches are scavengers and will eat pretty much anything. They have chewing mouthparts and would have little trouble dismembering another roach.