The altimeter deos not know anything about the mountain, so cannot take it into account.
Altimeter corrections should always be applied AGL where this is operationally taken as runway elevation.
The corrections are then applied to any value below MSA entires in the FMC which need upwards correcting.
If your landing runway would be at 5000', then the perceived QHN pressure reported for that runway would read accurately 5000' when on the ground. Once above it, cold weather corrections are applied.
However, if your landing runway would be at 0', then the perceived pressure reported for that runway would read accurately 0' when on the ground, and when cold weather corrections are then applied to the 5000' referred to earlier, altimeter readings would underread actual altitude by 200' (by your calculation of 4%).
So you see, it does not just depend on temperature, it also depends on where the accurate reference datum is from.
Thus when flying over the mountain with a correct pressure reading at the top, would only need altimeter adjustments for 2000'. However when referring to the pressure reading from the airport at its base, much mroe needs to be added.