Hm, from what I remember of the Chicago arc, no, there is no option of the PC becoming Quaestor of Chicago. However, the entire arc is about as complicated and messy as one would expect of a Chicago crime story.
If I recall correctly, someone in Chicago is trying to unseat Quaestor O’ Donnell, claiming that he is corrupt and mad and deliberately endangering the Masquerade. The problem is that, while O’ Donnell is indeed said to be cruel but efficient, I do not recall there being any concrete proof that O’ Donnell is purposefully trying to risk the Masquerade, no evidence except the word of the one that is trying to supplant him.
From what I little else I can remember, one may never even learn that the one seeking to overthrow O’ Donnell is secretly being supported by Chicago’s senator, apparently using the instigator as a proxy/puppet. This particular senator happens to have high Perception/Auspex, so he communicates via telepathy without ever being physically seen, good enough to read the thoughts of the PC and glean things that they would not want others to know. In some paths, it is apparently possible for the Chicago senator to thus blackmail the PC into helping with the ousting of O’ Donnell.
As for the rest of my vague recollection, if one plays it through to the end, one can oust O’ Donnell without killing him by tricking him into fleeing Chicago. However, in doing so, the PC has made a very powerful and bitter enemy. Killing O’ Donnell is presumably no easier, as O’ Donnell is old enough to prefer Vivaldi and decry Mozart’s works as too new and radical for his tastes.
On the other hand, one does have the option of betraying the rebellion to O’ Donnell at the end, but in doing so, they have made a dangerous enemy of Chicago’s senator.
Either way, whether O’ Donnell or the instigator is the quaestor by the end, the PC temporarily gains their favor and stays for a time, but a misunderstanding spirals out of proportion and forces the PC to leave Chicago.
However, there is another way. There are multiple opportunities to simply flee Chicago before the conflict between O’ Donnell and the conspirators reaches a climax. Of course, choosing this route would not confer the benefits that would come with seeing the conspiracy through to the end or helping O’ Donnell quash it. Then again, it might also be safer than the other two paths.
I suppose that it remains to be seen whether these conspirators align with the Loyalists or not. As it is, my priest is a firm Loyalist himself, and with O’ Donnell likewise being a Loyalist, my priest, by default, has no desire or incentive to see him removed, especially not with how stressed and nervous my priest is about other Loyalist Quaestors that have been removed and/or replaced by Stone’s lackeys.