Comment by ericmj

Yes. But the "constant factor" will be very large, even larger than for traditional ray tracing, for some global illumination algorithms, even when you chose to only render a small part of the scene. For example photon mapping requires a pre-pass where you trace photons from the light source onto the scene, that means that reducing the pixel count doesn't decrease the time for the pre-pass. http://en.wikipedia.org/wiki/Photon_mapping