Not exactly, lowering tyre pressure increases rolling resistance. Evidently (so I have read), rolling resistance is determined by how quickly the side walls can flex back into shape, and that is not only controlled by how the tyre has been constructed but also by the pressure of the tyre. Rolling resistance is also affected by the pattern of the tyre on the ground, a thin tyre has a logitudial pattern as opposed to a widish pattern of a wider tyre, a wider tyre has less rolling resistance. So it is possible to run a wider tyre at a lower pressure and sacrifice some rolling resistance and take advantage of the wider tyre pattern to compensate, but it will also increase the longitudial pattern as well, its a fine art to get it right, I found its best to pump them up to maximum pressure, but you do still feel the extra comfort espcially over broken tarmac etc.
Somewhere online is a site with comparisons of loads of various tyres in different widths and pressures from all the tests they did on them but its hard to find.