What they sell and what they can deliver are two totally different things. Any delay at all on your first flight (and you can spend a half hour just driving around Chicago after you land to get to the gate) and you will miss the connection. It may be a perfectly legal connection in their system, that doesn't mean you will make it.

They will take care of you, but you don't know how long it will be before they have space for you. It could be the next flight out, but if those don't have space it could be the one after that, or the day after that or the next day, etc.

I would not book a connection that tight, I would book something allowing much more room for error so I don't have to worry about missing the connection and which middle seat in the last row seat they will put me in when they have space.