I was stuck overnight in Atlanta last week (before all of this) because they couldn't find a pilot. They had everyone sitting at the gate until 2am, when they finally gave up and rescheduled the flight for the next day.
They even ran out of hotel vouchers and were making people go 90 minutes away at 1 AM when the flight was scheduled (and took of at) 6.
3 hours of travel time, plus 20 minutes for hotel check-in, plus 15 minutes for checkout, plus 15 minutes for waiting for the shuttle x 2, plus 10 minutes of walking to the bus stop, and that's 4:15 before you even hit the pillow.
That would put you at 5:15 AM, 45 minutes before the plane departs. Delta recommends you be at the airport at least 2 hours before the plane departs. So by their own recommendations, there is no way this could work, even assuming you didn't even head up to the room.
Source: lots of 5:45 flights with the airport security opening at 5:15