My friend have a fridge with a broken door. Impossible to fix the door as the whole base is eaten by rust. I thought about lying the fridge horizontally and then just put the door on top of it, but would the pump/compressor survive that way?
Not sure about whether the pump/compressor will be ok, but I can say that you may have trouble with (gravity) drainage of condensation going to places it shouldn't, such as into electronic components or other metal components that will be damaged or corroded by it. It may also leave a wet patch on the floor (which may or may not matter, depending on the situation).
You may also have trouble with water accumulating inside the fridge if it can't drain away?
This may differ between models of fridge, but all fridges I have owned have a shallow evaporation tray at the back where condensation can drain to and evaporate. Clearly, when a fridge isn't upright, this system will not work as designed.
ps: I don't actually know where the water comes from that is channeled to the evaporation tray. If anyone else can explain, please do!