No, they can't. Under city ordinance, only city cabs can do that. If you check the websites of the big ones like American, you'll notice they publish rates between various burbs and ORD/MDW/downtown, but not between any of them. Notably, the fastest route (most of the time) between ORD and MDW is 294/55, outside city limits for most of the ride, but only city cabs can do it under the ordinance.