A heavily iced up evaporator coil will not defrost in a couple of hours unless the cover in the back of the freezer section is removed and the door left open until all the ice is melted. Otherwise only a little ice in the center of the coil will melt and the coils will just ice up again shortly.
The first thing that an untrained person will think if a refrigerator is not working properly is that it is low on "Freon". In 38 years of working in refrigeration, I have found that this is the case in less than 1 in 1000 frost free refrigerators because their sealed systems are so well built these days.
When there is heavy ice on the evaporator coil of a frost free refrigerator it means there is a defect in the defrost system. It could be a defective evaporator fan motor, timer, defrost heater, defrost thermostat, drain heater, plugged up drains, thermostat or simply leaving the door open for several hours.
I have been on over 100 service calls where the homeowner installed a tap valve (notorious for leaking) and added a shot of Freon, thinking that this was the problem,