Does my LED panel require a gap between it and the ceiling for cooling?
Like all types of lighting, The LEDs in LED panels generate much more heat than light. LEDs are more efficient than traditional incandescent lights and generate less heat but still generate a lot and are much much less tolerant of overheating.

The 600x600 panels are designed for standard suspended ceilings as used in offices - there will normally be a large air gap above them, certainly tens of cm.

Therefore I would be very cautious about mounting them directly to a ceiling with no air gap above the panel. I'd expect a considerably shortened life for the LED panels and the possibility of at least minor heat damage to the ceiling.

Heat may degrade your adhesive and cause it to fail and potentially cause injuries to anyone below. I note that No-More-Nails have only one product that is advertised as "temperature resistant" and even that is only good up to 90C. I suspect their "original" product will fail at much lower temperatures.