Not really, unless you think illegals have Constitutional rights. Oh, shit, I bet you do.
Certain ones, yes; there is no "citizen" specification in certain parts of the Bill of Rights. One example demonstrating this is the trial of Standing Bear v. Crook, in which the US Government argued that Native Americans were, "not persons within the meaning of the law" and thus not entitled to things like habeas corpus and such. Judge Dundy ruled that in fact, Native Americare are indeed "persons" within the meaning of the law and thus do possess those rights. Since Native Americans were not generally considered "US citizens" back then, this matters.
The key here is, "following the laws". By definition, of course, illegal immigrants are not following the laws that say that one must come here, and be here, within the law. With that said, I wonder if the simple act of being here illegally deprives one of "certain unalienable rights", i. e. the right to a speedy trial, Miranda, habeus corpus, all that. IANAL, but from what I can see, it does not.
Just as big a question here is the one that GreenT pointed out. How do you tell by sight if a person is here legally or not?
So much for public education.
Indeed, because I learned the above in public schools. :-)