I always get dropped off at all 4 parks with no problem....for MGM, Epcot, and AK, you follow the handicapped blue line on the road, and drop off at the front of the parking lot. If a cast member stops you (this mostly happens at AK), just tell them you are dropping off. For the MK, either I have someone drop me off on the street by the Contemporary, so I can just walk in, or there is a drop off for the TTC - go thru the MK gates, stay in the far right lane (towards the MK resorts), turn left at the first stop light, and you can either drop off at the kennel or the small TTC parking lot where the cabs go.
I don't know if you have to pay for parking or not to drop off. I have a PAP, so parking is included. Hope this helps!