Oh yes, absolutely!
I think Luke’s idea of his mother growing up was very abstract, precisely because his aunt and uncle told him she was an off-worlder, and likely a rich off-worlder at that. He could never quite conceptualize that. And then he met Leia, herself a rich off-worlder, and suddenly, his hazy image of his mother looked a lot like her. (Later, when he found out, he would have a good long laugh about this.)
I suspect the revelation for Leia was much further reaching, though.
For one thing, I think Leia probably believed that slavery was another of the evils instituted by the Empire, and that in the days of the Republic slavery was illegal (it was, technically) and that those laws were enforced and there were no slaves.
Now, I grant you there are two possible ways to understand Tatooine’s political situation in relation to the old Republic. They are:
1. Tatooine (and the rest of the Outer Rim territories?) is literally outside of the Republic, and either a part of some Hutt empire, or else an unaffiliated world dominated by particular Hutts.
2. The Outer Rim Territories (of which Tatooine is a part) are just that - territories of the Republic. They technically belong to the Republic, but their people are second class citizens, and the laws are sparsely enforced, if at all. There is probably a long history of imperialism, violence, and exploitation. (For a real world comparison, consider the relationship between the USA and its territories in Puerto Rico, the US Virigin Islands, Guam, American Samoa, etc.)
My personal headcanon is option 2. It makes more sense of Shmi’s bitterness when she says “The Republic doesn’t exist out here,” and of Padme’s shock at discovering the Republic’s anti-slavery laws aren’t enforced on Tatooine. It also makes Anakin’s introduction into the Republic much more believable (if Tatooine was entirely outside the Republic, how exactly is Qui-Gon getting away with bringing an undocumented illegal immigrant into the Republic and expecting him to be trained as a Jedi?).
But one of the things that means is that, yes, slavery did exist under the old Republic, and was in fact tacitly condoned, both by the Senate and by the Jedi (because they knew what was happening in the Outer Rim Territories and did nothing about it).
And I think that would be the greatest difficulty for Leia in learning that her birth father and grandmother were slaves. Not just that she can’t really conceptualize that (she can’t, though after Jabba she has a much clearer idea), but that admitting it causes her idealized image of the old Republic to crumble.
In a way, that’s almost like Leia’s Bespin. Luke never had an idealized image of the Republic - his investment in the Rebellion was always more personal than strictly political, and I suspect that, growing up on Tatooine, he didn’t have a whole lot of illusions about the Republic to dispel. For Luke, the idealized image that had to be shattered was his image of his father. For Leia, though, I think it was her image of the Republic. And it’s fitting, maybe, that Anakin was the trigger for both of them to go on this journey, to kill their idols in order to more fully engage with the reality of the world.