We stayed there for a few days and I was able to leave my vehicle there longer then we actually stayed there. I coordinated with the front desk and they did not have an issue with it. it was not a busy time of the year however so it way depend on when you are planning on staying.
All I know is that as long as you are booked in a room, you can park in their lot. They are a great hotel that probably stays booked plus being so close to the airport, I would doubt that they offer free parking. Most of the hotels in the area do not.
Get an answer from Residence Inn Kansas City Airport staff and past guests.