I don't think your plan will fly - pun intended.

DTW is a 24 hour airport insofar as it is available for operations around the clock. With regards to scheduled services, however, there's a big gap, and I believe airport police will tell you that you have no business on a concourse. Today (for reference) Delta's last scheduled departure is a 10:38PM to AMS, and last in-bound a 12:30AM arrival from ATL. Tomorrow's first outbound is a 6AM to ATL.

There are numerous 2* (and below) airport hotels with shuttles. On a good night $90+ tax will even put you at the Sheraton.