Kind of a tricky question.
If the empires disappeared overnight, I'm pretty sure nothing would be lost with Sak, and if anything, she'd be overjoyed at the ability to raid places like Dodixie or Jita, especially in the early days with the collapse of highsec. Delicious carebear loot awaits!
Her sisters, while a bit more dependent on the empires financially, generally don't associate with the ideology of the places they live, so the impact would probably be minimal on their personalities. I think the sole exception to that would be Ereka, who's arguably the most pro-faction of the lot with her support for the Fed, especially considering how much her people have thrown a wrench* into the whole thing. She'd probably end up cynical and jaded, realizing that nothing lasts forever, even though she should have known that from the beginning.
* Think about this, for a second. Imagine the Caldari had found a way to play nice with the Gallente, Intaki, Mannar, etc. as members of the Federation. Imagine the progress that could have been made instead of the decades of war, the integrated Fed could have been a bulwark of peace and common interests in the galactic north, as powerful or moreso than the Amarrians. Instead, the Caldari did what Caldari do best, and look after their own self-interests, fucking up the whole attempt at "many cultures, one government". Ereka Nihil, arguably one of the most Caldari-hating Caldari out there, trying to make things right.