1. Create a dummy objective called Test
2. Set your score for objective Test to 1
3. Perform this command:

   /setblock ~ ~ ~ standing_sign 0 replace {Text1:"{\"score\":{\"objective\":\"Test\",\"name\":\"@p\"}}"}
   

4. Set your score to 2
5. Do NBT Copy on the sign (middle mouse wheel and ctrl) and place it down

You will notice that the sign has still the old value (1) instead of the new (2) even if this sign was new placed

I am not sure if this is intended but I guess not