That would pretty much stick a fork in the 1st and 4th Amendments, even if you think the Constitution only applies for legal residents.
Forced checking without probable cause would violate the Constitution. But how bout someone asking “Are you proud to be a Mexican citizen? Yes? Do you think you’ll ever become a legal resident of the USA?
Anything other than “I already am.” Yes, no or whatever gets an instant free pair of bracelets.
So why would the United States Constitution apply to invaders?
There is “probable cause” to check status of protesters simply due to the fact they are protesting the checking of status. Are you saying the Feds are violating the rights of those people whose company gets raided?