The way I read it, a registry would be legal. It would be an administrative procedure. Read the underlined portion. It is mine. Much of what could be used to deport an immigrant is already in place. Remember, they are talking about immigration matters, not criminal proceedings.
Do Noncitizens Have Constitutional Rights?
But
immigration proceedings are matters of administrative law, not criminal law. (As a result, the consequence of violating your immigration status is not jail but deportation.)
Still, immigrants facing deportation do have some rights. Most are entitled to a hearing before an immigration judge, representation by a lawyer (but not one that's paid for by the government), and interpretation for non-English-speakers. The government must provide "clear and convincing" evidence to deport someone (a lower standard than "beyond a reasonable doubt").
But the Alien Terrorist Removal Court has never been used, and a Department of Justice spokesman said he isn't aware of any plans to use the terrorist court any time soon.