When the elders "approve" someone for baptism, it is tantamount to saying that this person has sufficient knowledge of (their version of) the teachings of the Bible to commit to living by them and that this person is therefore acceptable as a member of the congregation. All other aspects of the baptismal candidate's life (living arrangements, "acceptable" employment, sexual orientation, marital status, etc.) have been delved into and determined to meet JW standards so that the candidate doesn't bring reproach on the organization Jehovah's name.
I agree that the organization has no legal obligation to inquire into an individual's immigration status even though they certainly inquire into everything else. But if it is known that the person is willfully breaking "Caesar's laws" on an ongoing basis, ignoring that fact by accepting them for baptism and presenting them to other JW's and the world as law-abiding Christians constitutes tacit approval and endorsement of their actions.
I say this because while the JW's claim that baptism is merely an outward sign of one's personal dedication to God and the commitment to do his will, it is actually a de facto initiation into the Watchtower Society, regardless of how they phrase it or what organizational name they use. The JW baptismal "vows" no longer offer even a pretense that the candidate is being baptized in the name of "the Father, the Son, and the Holy Spirit." It is much more like a swearing-in ceremony than a traditional Christian baptism.
I believe there are two main reasons the elders are told not to consider a baptismal candidate's immigration status when deciding whether to approve them for baptism. First, most of what little growth there is in the West and particularly in the US is among Hispanics and it appears that a disproportionate number of those are "undocumented." The Society needs all the new members it can get (to boost their numbers), and can't afford to turn away whole groups of potential guileless victims converts. Second, if it became widely known that JW's were "withholding baptism" on the basis of a person's legal immigration status, it would probably generate a lot of bad publicity and the backlash could be dramatic. Certain cities or companies might refuse to rent them facilities for their precious (and moneymaking) conventions. I have no doubt that certain of the media would be positively apoplectic. It would be the height of political incorrectness. I can hear it now: "Principle be damned! We gotta protect our money reputation!"
In at least one instance, elders were instructed in writing and on official Watchtower stationery to accept for baptism a self-confessed murderer who was even at that time a fugitive from the law. While I accept that elders are not the police and it is not their place to investigate crime and enforce Caesar's laws, it sure seems odd to me that the organization would want to be complicit in cloaking such a person with the appearance of living (their version of) a Christian life.
Especially when they are so quick to denounce and shun an otherwise exemplary member whose only "sin" is to question any Watchtower doctrine, interpretation, or policy, however mercurial and self-serving it may be. Now that's hypocrisy on an industrial scale.