How late is your "prior commitment?"
Several years ago, we flew out of Indianapolis. We stayed overnight at (I think it was the) Days Inn and took advantage of its park sleep and fly program (actually cheaper than just parking at an off-site parking lot).
Due to an unexpected problem at work, we didn't leave Greater Cincinnati until almost 8 PM. Got to Indy about 10. Checked in and still had a good night's sleep. Granted, our plane didn't take off until about 10:30 the following morning, but we were all up by 7, anxious to get going.
Honestly, the only way I wouldn't do a park sleep and fly out of Indy is if I didn't get to bed the night before. I'd be worried about car problems/traffic going up I-74. And even if you didn't get to Indy until midnight, and your plane took off at 8, you can still get about 5 1/2 to 6 hours of sleep. And did I say, the park sleep and fly could be cheaper than just parking off-site?