I had a 6:30am flight at mci the other week and woke up an hour late and I checked my bag (international final destination) at 6:19, strolled through tsa precheck and walked to the gate. Last one on the plane and door shut at 6:25. Thought I would have to have a middle seat but the row I picked was a couple so the dude moved to the middle and gave me the aisle. The next leg was only 1/3rd full so I got the entire row to myself. The bag check said it would be a day late because of late check-in, but it was waiting for me after getting through immigration.
No negative consequences