To refresh: Nietzsche's story in the Genealogy of Morals involves the oppressed turning in on themselves for satisfaction, because they can't get satisfaction in the usual brutish, masterful way. Nietzsche is often taken in telling this story to be advocating the master morality, and certainly he does explicitly rail against the content of this slave morality (Christianity), but in the Genealogy, he really is trying to give a "scientific," i.e. historical, account, and in the Gay Science and elsewhere, he stresses that the turn inward made us interesting, gave us the self-reflective capacity that now makes philosophy possible.
Hegel was likewise trying to give something like a historical/psychological account, in that instead of a social contract starting off society, we get one person enslaving another. While Hegel doesn't say much more about the master, the slave in this equation is the one who works directly with the real world, and who also gains a view of himself, i.e. in how the master sees him (the master doesn't give a crap about how the slave sees him on this account; the slave is just a tool to the master). In both of these ways, the slave "gains a self." Now, someone else will have to fill me in re. the degree to which Hegel spells out the steps by which this self-consciousness then becomes a dominant part of the social zeitgeist (if it ever does at all); my memory of Hegel if fuzzy on this point.
My point here, though, is that both of these points, and many of Nietzsche's other comments in Gay Science, seem to make suffering and subjugation not only a necessary, historical evil for human development but a positive boon on the individual level. My immediate reaction is to push on both of these thinkers my own view that, no, of course not; none of this should deter our efforts to eliminate suffering. True, were we to actually achieve a state of no suffering on a social level, then we would have to contend with becoming the "last man" in Nietzsche's sense, which I think of as equivalent to the people lying around on couches in Wall-E. But since there's no real danger of succeeding in the effort to eliminate suffering, the goal of reducing suffering remains pressing and obvious.
This dynamic is comparable to the one engendered by contemplating Heraclitus's picture of the world as conflict: that the tension of opposing forces is what gives society and even the physical world a definite character and sustained form. Both this and Nietzsche's exhortation that suffering breeds character might lead one, as a political and/or ethical matter, to posit that we're better off leaving people's fates to their own struggles and the winds of fate (i.e. chance) rather than to a social plan designed to mitigate suffering.
Whatever your meta-ethical views (i.e. whether you think ethical principles are pure human inventions or have an objective status or both or neither), the prima facie desirability of reducing suffering is a basic ethical principle. Without pretending that this intuition amounts to a fully detailed principle (Should we always act to reduce suffering? Whose job is it to reduce suffering for whom? How do we balance reduction of suffering vs. other goods?), I think we can safely say that it's part of a default ethical framework for beings like us, meaning that you don't overturn it unless you've got a damned good reason. On the Buddhism and naturalism episode we asked "why would belief in no-self lead to compassion?" A simple answer is that compassion is the default and that no-self is not sufficient to overturn it, while no-self is sufficient to overturn avarice and pride and other things that would ordinarily interfere with compassion.
Nietzsche's "ethics" is, as we've discussed, a matter of "I will," not "thou shalt." Because he also thinks we're pretty ignorant of ourselves, there's no reason that he couldn't give you some advice about your life if he knew you well, but he seems fairly unconcerned with the project of translating this kind of ethical deliberation into legislation. Given the complexities of his ethical view, i.e. the differences between people in what they need at a given time, I'd guess that he'd see legislation as necessarily divorced from this complex personal calculus, relying instead on more crude principles: pragmatism, or perhaps utilitarianism, or maybe something else. One could argue for a variety of legislative systems as compatible with Nietzsche's insights, but surely we'd need some form of freedom to be central to it: freedom without which individuals would have no hope of self-actualizing.
This conception of freedom might be libertarian--"everyone has the freedom to pursue happiness"--or it might be the kind Frithjof in New Work deliberations ties explicitly to Nietzsche, where positive steps are taken (surely by government, but not only by government) to liberate us in a real way from drudgery. But on no account would Nietzsche's view support positive oppression on the grounds that being oppressed would make one stronger, or more interesting, or better suited to philosophy. Nature (including our own psychology) gives us many unavoidable challenges, and if we need more than that, then we can think up challenges for ourselves. As an expression of "I will," I might choose to pursue a challenging, even dangerous path and be all the better for it, but Nietzsche is in no position to recommend that we actively try to put others at a disadvantage for their own good. Feeling good about being oppressed (a "slave party," if you will) is clearly a post hoc rationalization, a form of amor fati, where you accept what has come to you as yours like a good existentialist.