Cook County is very similar to Winter's Bone for sure. I'm not saying it can generate Winter's Bone money but they definitely have the same story. That would be pretty sweet though.
An Academy Award nomination is the promotion. I, personally, don't really expect the one week qualifying run to generate any significant money. The run just qualifies the film for awards consideration this year. If Anson Mount can get a best actor nomination, and by all accounts his performance is amazing, or Cook County can garner a nomination in another category then we can expect a decent showing all around due to the world wide awards ceremony exposure. If not then DVD's will still do well enough...
Id definitely be curious to find out how they are currently promoting it.