I know a JW personally who used to be a Circuit Overseer for Spanish-speaking circuits. I asked him one time about this very issue.
His answer was: WT does nothing about illegal immigrant JWs in the cong. Illegals cannot hold any position in the congregation, but neither WT nor the local elders sees any need to tell these people to conform to the law of the land. I asked him how WT could take such a cavalier approach on this when they brag about how JWs are exemplary in following Caesar's law? His only response was a shrug.
The WT quote posted by Blondie is very clever ruse by WT. It uses the example of a non-JW Bible study who's an illegal. The fact of the matter is, WT takes the same nonchalant attitude with baptized JWs who break immigration laws too.