I don't know* whether the Constitution applies to illegal aliens or not, but if it does I think it should apply 100% - not just partially. The document was not designed to allow rulers to pick and choose which sections apply and which do not.
* I suppose the question of whether it applies is based on which conditions you must meet for it to apply. Obviously the Constitution only applies on US territory. So given that a person is on US territory, does that person have to be a US citizen to be protected by the constitution, or does just occupying a spot on US land afford a person constitutional protection?