She'll think about this while doing the not-necromancy stuff.
If they're giving citizenship to anyone who shows up, this is not the sort of oath where they expect you to be Lawfully binding your future self by swearing it. That doesn't mean she'll ignore it, but it does mean it wouldn't be betraying a trust she was given, only no longer holding to what she believed about the Imperium. She won't make this unless she concludes she in fact supports them, because otherwise she wouldn't mean it, but it would count as meaning it to support what she now knows about the Imperium, and if it turns out that actually this is like Cheliax, she can Lawfully say that she did in fact think that the Imperium was the sort of thing she'd support, she no longer thinks that, and publicly resign her citizenship before doing anything to oppose them.
Given that, what does she know about the Imperium so far? Random people who're asked for directions from strangers spend a few minutes helping them, they have nice parks (it's at least something), you get citizenship by asking for it, there was that sense of safety in the beginning but there's no reason to think snake-based involuntary transport is on her side here (although it did apparently teach her the language), and they're apparently mostly catfolk but that doesn't really matter one way or the other. That does sounds like the sort of place she'd be fine with. Kaiser sounds suspiciously like a non-elected title but Lastwall isn't a democracy and they banned slavery seven hundred years before Andoran did. She'll want to spend a while in a library to confirm things but she's provisionally on board.
The text of the oath......allegiance is pretty clearly a statement of intent, she so far in fact supports them. Obeying the laws she will in fact do unless and until she decides that the government is not in fact legitimate, in which case she'll renounce citizenship first. She'll protect her fellow citizens whether she swears to or not. Fighting in their battles she'd do unless, again, she decided she didn't support them. It also doesn't specify that she'll do it on their side but she's not that kind of somehow-technically-Lawful. The Kaiser should live a long life unless he doesn't want to.
She'll swear this.