Here in Chicago it is very important to know what the city policy is. This city runs on city policy! For better or worse. And, stuff left in public places isn't allowed to just sit there for indefinite periods of time. If I were going on a two week ... much less two month ... vacation I wouldn't leave something on public property expecting it to be there when I return. I don't know how it is in DC, but here in Chicago, folks don't like junk hanging around.
Shiek, you may not care what city policy is ... but Koffee has the Chicago policy, which affects this situation, right.
The only thing I'd add is if the rack is on private property, the owner of the property might have to say something to the cops about the bike, it's abandonment, or wanting it cut off. Personally, I'm not sure if I'd leave the note or have the cops do it, but I'd go with one or the other giving the person a couple weeks notice and then get that bike back to a useful life.