If you read the court decision it's clear that ICE kind of IS trying to do that. They seem to have reason to believe that there are certain men at a specific shelter who illegally entered the United States that are operating under a false names who have committed one of 8 specific "serious crimes" (murder, manslaughter, rape, robbery, assault, grand larceny, burglary, and assault of a law enforcement officer.)
What they want is for NYC to produce the list of males at a certain homeless facility in a certain age range along with their previous or current criminal convictions so they can tie the fake names to the real ones they are looking for.
I'm not sure I agree with what ICE is doing but it's far less intrusive and reaching than what the headline suggests.
Interesting to note that parts of the decision are redacted and that the unredacted version will be filed under seal.