What exactly are you trying to test on the board?
If you are only checking continuity (ie copper goes from point a to point b and there are no breaks)..........you can certainly pierce the plastic overlay of the board without doing any damage. I would suggest that you use a pin or needle and connect your "probe" to that and then use the pin to connect to the copper, this way you do as little damage to the plastic coating as possible. Depending on the size of the copper "run" you may be able to scratch the surface, just make sure you reseal it so it doesn't create any shorts when you put it back in.
You can check "signals" using the same method but again I go back to what are you looking for in the first place? :confused