For an atomic nucleus (more complicated than [sup]1[/sup]H, anyway) is it more correct to think of it as a bound collection of discrete particles (the standard textbook drawing of a bunch of attached marbles), or as a distinct entity different than its constituent parts? I.e., is a [sup]12[/sup]C nucleus adequately described as six protons and six neutrons, or is it more of a single conglomeration of 36 quarks? Do the quark partnerships change in this larger entity, or do they remain bound in their original groups? Is this even a meaningful question? 
It’s definitely a better approximation to think of them as remaining distinct protons and neutrons.
That said, there are several things that blur their identities. For a start, all the protons are indistinguishable from each other and so are the neutrons. And that has various quantum mechanical consequences. It’s a bit difficult to say “that quark remains in that proton” when you can’t even keep track of which proton is which.
Furthermore, the whole thing keeps together because of interactions between the nucleons and these interactions involve the exchange of quarks and gluons. However, one reasonably good way of describing this is that they don’t swap individual quarks, they swap pairs of them in the form of particles called pions.
Quarks in a nucleus never deconfine; they’re always associated with at least one other quark in the form of some larger particle. There is believed to be a state of matter called a quark-gluon plasma where that rule breaks down and you get something like your “conglomeration”. But that can only happen in much more extreme conditions than you find inside nuclei.