Can the discharge when plugging a laptop to a power outlet can do any harm?
The spark is just the capacitor in the input stage after the rectifier charging up. That is common for a switching power supply, unless the designer put extra effort towards limiting that inrush current.

This can not overload the power supply, it just charges up to normal operating conditions. The input capacitor can't get more voltage than the outlet provides. Can the spark erode the contacts? Maybe, I don't know (these aren't exactly flimsy contacts), but my feeling is that you would face mechanical failure from all the plugging long before that could even become a concern.

The reason that you don't see and hear a spark without the laptop connected could simply be that it is too short and weak when it is only charging that capacitor. The connected laptop, on the other hand, might immediately draw enough current from the outlet through the supply to maintain the spark until the plug is fully connected.