No, the emphasized portion does not LITERALLY do that. Since the Bill of Rights previously constrained only the Federal government, there was no privilege or immunity held by the person vis a vis the state governments. The second sentence is correct. But, the 14th Amendment isn't simply an add on that takes effect from that point in the document. The amendment changes the entirety of the document. So, literally speaking, it established that the bill of rights applied to all citizens and forbade the states from jerking around with em.
In fact, even now the Court doesn't apply those protections through the Privileges and Immunity clause. They are all incorporated through the due processes clauses. Honestly, I am not worried about the court. They very often try to use Algebra to come up with 2+2=5. I am speaking only from my own knowlege and study. And, I don't claim to be anything other than an interested layman. That happens to be why I welcome disagreements. It allows the ol brain housing group to expand a bit.
And in fact early on the Bill of Rights was not incorporated through the 14th amendment at all. It was only later that the Court reversed itself and started interpreting the 14th amendment that way.
The incorporation is anything but literal. A 'literal' wording would say something to the effect of "the guarantees of such and such amendment are hereby applied to state and local government." Or any of a multitude of different ways you could write a literal incorporation. The 14th amendment is not anywhere a "literal" incorporation. From what I have read of the popular media of the day, including diaries and letters, the wording was in the colloquial syntax. Just because we (the 21 Century thinkers) would word it differently doesn't mean it isn't a literal statement.
I should add that the 'literalists' are the ones on the Court who refused to incorporate the Bill of Rights early on. They took the position that if it was supposed to incorporate the Bill of Rights it would have said so. I wish those guys had been as literal when the commerce clause got stretched out of shape. Yeah I know that is off topic, but it still peeves me.
The Bill of Rights only gets incorporated when the Court moves away from literalism and tries to discern the 'intent' of the drafters and also pulls public policy considerations into it. In fact, they are largely pulling in public policy considerations when they do the incorporation time and again, not resting on the literal reading of the 14th.