What is the significance of finding quark-antiquark pairs in hadrons? What is the significance of finding quark-antiquark pairs in hadrons?  Does is have any effect, and hypothetically, could you pull the 3 quarks in a hadron apart so they formed 3 mesons?
 A: Your putative logical opposites are not as incompatible as you are imagining. Through the magic of the Dirac equations involved in QCD, the gluons, that must be in the hadron to bind the quarks together, split into quark-antiquark pairs all the time. 
So, even if you did not "have" quark antiquark pairs in the hadron, pulling  the three quarks apart will increase the effective intensity of the gluon field precipitously (think of them as 3 rubber bands joined together), and it would "break down" to quark antiquark pairs (in some analogy of a hyper-intense EM field breaking down to electron-positron pairs), with the antiquarks dressing your pulled quarks to form mesons, and the quarks combining with other emergent quark-antiquark pairs to form ("hadronize to") a spray of hadrons (jets). This is what happens in a hadronic collision, in a way, even though you do have quark-antiquark pairs around: they do not modify this qualitatively. 
But the virtual quark-antiquark pairs you have in a hadron are incessantly roiling and bubbling into and out of the (QCD) vacuum all the time: one yoctosecond you see the pair, and the next you don't. So you can't think of the hadron as a jar full of a fixed number of marbles in it. 
This "sea" of quark-antiquark pairs can be measured quite well in scattering experiments, and features of them and their parent/grave gluons determined. They modify asymptotic freedom (the force property that makes the gluon field grow, above), and chiral symmetry breaking, the feature that gives a baryon and a meson its mass. 
These pairs are co-equal partners with the gluons and your initial "valence" quarks in putting the strong interaction dynamics together. 
