I tend to agree with keyguru, those spots aren't necessarily for long term parking. Though I don't think anyone is stopping you from using them for your purpose.
However, there might be some 15A circuits available in the airport parking garage. The Little Rock airport has this and we're nowhere near as cool as MCO

I'm not seeing anything on PlugShare.com though. Might be worth driving around the parking deck looking for outlets on support posts - I've found them in many parking garages. Remember to park in such a way that your mobile connector and cable are not in anyone's way and hopefully as discrete as possible.
As for it continuing to charge or not, the car draws power from the charger. The charger does not push power to the car. The car will stop drawing power when it has reached its charge setting. I recommend 80-85% for long term storage.
As for cost - a parked Tesla even with every parked setting enabled (climate monitoring, sentry, etc) won't use more than probably 20kWh per day. At 12¢/kWh you probably won't have more than $10 for the whole visit. If for some fluke reason your car draws maximum power from that charger the entire time it's plugged in the maximum charger I'm calculating would be about $222. I'd be impressed if you could do that
