I think the answer to my question is no, but I can't find an explicit statement about this on my books or online.
I know that gluons are the vector bosons for QCD, the $SU(3)$ gauge theory of color, and they come in $3^2-1=8$ different types, and they have interactions with themselves and with quarks, which are the only particles that aren't in the singlet representation of the $SU(3)$ color group. My question is: if there was only one quark, say the up quark, would gluons care? I wonder this because it's often said that the strong force "keeps quarks together inside nucleons" but from what I understand it doesn't necessarily mix the flavors and could easily create, say, a three-up-proton with charge $+2e$.
I read this question but it doesn't answer my doubt: I know that, since there are many flavors of quarks, the gluon can interact with all of them, my doubt is whether the gluons need so many different flavors to work, if I need to consider all of them to make a $SU(3)$ theory work.