In short, it's complicated. Technically, the AH stadium would result in the Bears paying property taxes where they are currently paying none, so in that regard, it would increase the tax revenue. There also is the issue of the tax burden increasing for the local area, especially if AH has to shift it to homeowners if the Bears are paying a substantially lower amount, which is a fantastic way to piss off the locals.
So, the question that should be asked is, if the AH site were instead developed as residential/commercial, say like the Glenview Naval Air Station, would that be more beneficial to AH, Cook County, and Illinois than a massive stadium complex? That site won't remain vacant for long if the Bears pull up stakes and move to Hammond, so it's a valid question.