^ I guess our point is, does it even matter?
The short answer, I don't know. My guess is that by virtue of the station being mothballed, there will not be fully functional trackage through the station, as this would involve not only the tracks but the traction power system and the signalization of both interlockings (State St and Dearborn St); after everything is excavated/demo'd, I don't see why such things couldn't be added at a later date. There would be some value in having at least one track connection complete to support fleet moves, as right now the only place the Blue Line is connected to Skokie Shops is via the Paulina Connector, but I'm not sure if that alone is worth the value of installing the track and the accompanying infrastructure at this point.
If a private operator could get a (contractual) promise that I-90 will never be widened, I wouldn't be surprised if there would be some interest in a public-private partnership that would involve the private sector kicking in at least some portion of capital costs for express trackage and terminal modifications. From what I've heard, there are already presently on the order of 2000-4000 air travelers daily going from downtown to O'hare on the Blue Line, which is a substantial potential market particularly if travel times by car/van to O'hare can only be expected to increase.
Express service to Midway is a trickier proposition: the volume is less (though the transit mode share for airport trips is better), but the Orange Line is already incredibly fast and already competitive with taxi service: it's only 19 minutes from Roosevelt to Midway station (hence the already solid mode share for such travelers). The only thing a Midway Express service could offer over local service is a much better DCA/National-style connection to the terminal (rather than the current circuitous and unpleasant walkway system). But the capital cost for such a terminal rail station, elevated over Cicero Avenue with accompanying modifications to the existing terminal, would far outweigh the potential revenue from the express service, so it seems like a non-starter.
This is why the Airport Express operational concept anchored at B37, as conceived, is well, ill-conceived: it is dependent on express service to both airports, cycling through the station. O'Hare is the only airport for which there exists a plausible potential market (and thus, potential private sector investment interest) for premium-priced express service.
B37 would have still played a role in an O'hare-only Airport Express concept; as an 8-car siding for express trains to pull into after discharging passengers at Clark/Lake, to turn around and head back, picking up passengers at Clark/Lake. Use the Loop Transportation Center (203 LaSalle) for it's intending purpose as a full-featured Airport Express terminal with downtown check-in, baggage check, rental cars, etc, modifying Clark/Lake station for the various required baggage facilities. Given the lower volume, premium fare surcharge would simply be collected on the train, a la Metra, so little to no modification of Clark/Lake fare arrays are required.
The B37 concept would still involve improving the Washington transfer facilities between the Blue and Red Lines; heck, even put a single platform along the B37 siding to allow discharge of passengers for transfer to the Red Line, the one transfer they can't make at Clark/Lake. But you DON'T build a track connection with the Red Line, because you DON'T run express service to Midway and you make do with the Paulina Connector for fleet moves. And these track connections, which involve mining alongside a live railroad amongst a hundred years of buried utility lines, are the major, major cost drivers of this project.
By eliminating the Midway Express pipe dream, you also reduce the specialized vehicle requirement, as well.
But I guess it's a bit late for all that...so what on earth do you do with the station now?