Firstly, what is your objective?
If you want to eventually get a job in the Chicago area, you might want to consider leaving for fellowship. The problem with cities such as Chicago and Boston is that there are many institutions fighting over the same pie, so there's a good chance you'd end up with a skewed perspective if you did all your training in that local area. For the sake of career advancement, you'd have a better chance of a well-rounded experience if you go to a high-volume surg path fellowship with a strong reputation. Mayo for instance has a great reputation throughout the Midwest if not more, and doesn't appear to have a problem placing their fellows, even those with "just" surg path (although I don't know if many of the latter are heading to popular places like Chicago).
I can't say I'd recommend paying someone to let you be their surg path/cytopath fellow. Those two fellowships are nowhere near as competitive as say dermpath (for which I have heard of rare arrangements to be unpaid fellows). I suspect that being an unpaid surg path/cytopath fellow might do some damage to your reputation, as it is not a common path to take - and in addition might cast doubts on the candidate's skills and abilities. But others might think different.
As for whether an unpaid fellowship is an ACGME violation - ACGME only accredits the structure/content of fellowships, so if you found an institution that was willing to do all this wading into uncharted territory for you (I can't imagine that it would happen without a lot of string-pulling and money changing hands) I think it could be done right. Whether you could sit for cytopath boards is another question. Presumably the people who did unpaid dermpath fellowships did end up taking dermpath boards, so based on that I guess it's fair to come to the conclusion that the same could be managed for cytopathology. Seems pretty fraught with risk.
If your goal is to stay in Chicago no matter what, I would call around and keep an eye open and an ear to the ground for any unexpected openings. I don't personally know of any, but check PathologyOutlines.com and CareerMD.com etc. And be prepared to move if you have to.
[EDIT] For what it's worth, I think UMinn has cytopath spots open for 2010.