That's how it's used sometimes, but do you find this used often enough to even be worth talking about?
More often, from what I've seen (granting that I am not omniscient so my perspective may be limited--and that it gets hard to stomach the endless drivel from right wing propaganda that is so misinformed as to not even be lies, so I'm especially underinformed about the exact details of their nonsense), the argument is dismissive of the single mother who isn't advocating for better schools but who acts like she doesn't care about schools (the argument being that she doesn't care because of a victim mentality--which may also be wrong, but if so you need a different argument against it).
So while I completely agree with your argument here given the premises, it seems to me that you're mostly arguing against a straw man.
Indeed, the people who argue against a victim mentality tend to point to the same kind of studies that you just did: get into a virtuous cycle of education and achievement instead of acting the part of a victim.
You haven't really argued against that perspective at all--and isn't that the main one?
(Possible arguments against: (1) the infrastructure is simply unavailable for many people or (2) it's all well and good to say so but that kind of willpower and drive doesn't come from nothing so you have to kick-start it somehow and until we see that magically happen we should just recognize the victimization and try to provide the oportunities that we can; possible additional arguments for: (1) stereotype threat dramatically decreases performance and being a victim is a stereotype or (2) students with a growth mentality tend to have better achievement and it's hard to simultaneously have a growth mentality and accept the view that one is a victim.)