You are not eligible for a greencard (and by extension, immigration hearing) if you have entered illegally.

The feds (ICE) do really like getting deportees at courthouses, especially criminal trials, because they are already handcuffed when going into or leaving the courtroom so they can just literally give the court officers the paperwork and take the deportee.

If these people are such valuable contributors, why do you insist on deprieving their home country of them?