While waiting for my connection (TE to LSL) in mid-April, I did some exploring around CUS. Returning to the station from Lake Michigan, I arrived at the Union Station Transit Center, a bus terminal across West Jackson from Union Station, and rather than wait for a walk light, I saw a sign directing me to a different way of crossing W Jackson. There was a flight of stairs and (I 100% thought) an elevator down to a subway station. The pathway from the bottom of the stairs through some doors led directly to the Grand Hall and I don't remember any steps at all, but there might have been a short flight. Off to the right was a subway station, but I have no idea what line it was and whether it connected to O'Hare or to a line that goes to O'Hare, or whether it was CTA, Metra or something else.
At the bottom of the stairs was the lower end of the elevator. I took the stairs, so I don't know if the elevator was actually available. It might have been new and not yet in service (the whole bus station looked pretty new), or it might have been out of service or not available to the public, or it might have been an old elevator in the process being removed.
The subway station should be totally accessible from CUS, just go through the doors on the south side of the Great Hall, and follow the corridor about 100 feet to the turnstiles for entering the subway station. I'm pretty sure it was level boarding.
The non-Chicago people answering this question so far seem to have even less current information that I do! There must be some Chicagoans here who are familiar with the current (construction-disrupted) setup and know exactly what this subway station is, what lines it serves, and whether it is useful for getting to and from O'Hare. Please chip in! I suspect the people from Chicago who have replied so far know all this and are assuming everyone else does as well, but we obviously are relative strangers and don't!