I suspect the routing is invalid no matter where you book it - CO, Expedia, etc. The only difference is that the CO website will only issue a single ticket per pax in an itinerary. I believe that if you booked this on Expedia you would find that it's issuing multiple tickets for each separate valid "block" of flights. You would be able to test this if you booked on Expedia, as it would show the ticket numbers that it has issued.

It raises the question of what would happen if there were any irregular ops. For example, if your ORD-EWR flight got delayed causing you to miss your EWR-ORD flight (assuming they were on separate tickets) I believe you would have no protection against this.

So overall the only benefit you would be getting here would be having a single receipt, and potentially there could be negatives to doing it. Personally I would just book multiple tickets and be done with it!