Test supply lead on its own, insulation test, earth bond , then treat power supply unit as SELV (Separated extra low voltage) and just do a visual inspection to make sure its not damaged/cracked or split open in any way or showing any signs of heat damage/overheating...
I wouldn't do a 250 volt test or a 500 volt test on a laptop power supply using an adapter plugged into it as you could pop the rectifier diodes inside or some capacitors, the cloverleaf is really for testing different types of leads i.e male/female cloverleaf to standard IEC type etc using a normal PAT testing lead or the IEC test socket on the testing machine...
advise user/owner when you are leaving the location that they should not cover any mains adapters, especially not laptop ones by for example leaving it in the bag/case with the lead running in and out of it or wedging it down the back/side of a filing cabinet etc...as these power supply units are designed to get rid of heat by re-radiating it from the case, they are designed to transfer heat from inside the case to the plastic on the outside...I know it does not sound sensible to transfer any heat to any kind of plastic but where else could it go on a plastic clad box....
There are chunky Aluminium or copper (depending on price) heat sinks inside to take the heat away from the transformer and the Regulator IC's which are bolted onto them and get it out of the case....
some Laptop adapters/chargers have cooling fans but these are generally replacement ones sold in the shops and are not usually very reliable compared to the ones made by the laptop manufacturers which are generally fully sealed in terms of having no holes or vent grilles on the case...they really do not want to block these kind of chargers...