Although the surface will now certainly be brighter on an absolute scale, is it possible that the additional lights illuminate other parts of the scene so much more than the spot in question that it now appears - to the naked eye for example - relatively darker?

Yes, relative to now brighter areas of the scene, areas that still experience little to no illumination will inevitably look darker.

Assuming we want our scene to model real life as accurately as possible, we can take a real world scenario. In the case that a flashlight is directed towards an object that was previously only indirectly lit by another light source, the shadow now becomes darker relative to its original shadow.