No. It just makes them not citizens. There is quite a substantial body of law covering the intersection of non-citizen residents and the constitution, and that would not change. -- After all, your interpretation of the Preamble would mean the Constitution only applies to citizens and their descendants --
Well, I was just stepping in where it was none of my business, and giving my take on what "PJ Too" was driving at. Anyway, as I said above, there is a substantial body of law, some in the nature of personal rights resting on the constitution, that governs the relationship of the US government, state governments, and non-citizens. See, for example, the recent festivities following Governor Brewer's attempt to regulate government action when police come in contact with those suspected of being in the country illegally.
But if all laws are founded in the Constitution - and the Constitution does not specify the rights or responsibilities or duties of non-citizens - then I don’t see how we can legally do anything with or restrict non-citizens.