Yes, this is my position by far and large.
Syndra is ambitious, but she is also selfish - ironically, in a very Ionian way. She would pursue rulership as a means of protecting herself, by creating a world in which she belongs to. It would only interest her in so far as removing the people and ideas that keep her (and people like her) repressed and worse. In its own round about way, rebalancing the unbalanced 'neutrality' enforced by the current order of affairs.
Born and raised Ionian, it's just the establishment she despises. A lot of the cultural nuance would remain, save what she'd throw out to suit her needs. With her much more aggressive mindset, she'd be incredibly appealing to wartorn Ionia, and those who were subjugated by Noxian brutality. So, there's a popular foot for her to stand on, enough to overlook her more eccentric aspects. Once secure in her own position of power as the undisputed Sovereign, she'd most likely leave Ionia to its own affairs afterward. Minutia is pointless to someone dedicated to their own bodily mastery, after all.
She just needs a world she can be left alone in.
Zed is actually a perfect double edged sword in this regard. Through her, he's given a purpose in a bigger picture - ninja have no meaning without someone to direct them. Killing for the sake of killing is simply murder, but killing to change is the art of assassination. It's unclear how stringently Zed would obey this line of logic, for he might simply also look to kill the strongest for 'a challenge'. He can go either way with this flexibility, making him quite the wildcard in Ionia's political atmosphere.
Over all, this ties in very nicely with Syndra's social commentary. She's Ionian, but she was nearly undone by the establishment, and has just (to her) reason to supplant it. She isn't a natural ruler, though, not enough to become something like King Jarvan or Boram Darkwill. Ionia just needs to be in a place to suit her whims when she wants it. In return, Ionia itself has the fickle protection of one of the world's most powerful mages.