Yes, your bag will be checked all the way to ORD. There are storage lockers at Copenhagen Central Station, approx USD 10 for 24 hours.

If you take the metro it will take you about 15 min to reach downtown Copenhagen. If you take the train you could be at Copenhagen Central St. in 12 min. Ticket is USD 5.50.

I would head back to the airport around 2PM (sooner if it rains!) - then you would still have some time (15min-½ hour) to enjoy the lounge before proceeding through passport control and to your gate (should take 10 min maximum from when you leave the lounge). CPH is really easy to navigate and walking is not far (from the lounge to the C gates).