Removing woody biomass will probably not reduce forest health and may actually improve it in some cases. There are a few points to consider for this answer. First, there are times when removing low-quality, diseased damaged or unwanted (or invasive) species might improve forest health. This removal may also be used to create openings suitable for replanting or for the natural regeneration of a more desirable species for income or wildlife. In this situation, removal of all of the woody biomass might be economically advantageous and also would contribute towards improving the overall forest health.
The second point to consider is that "woody biomass" is a term that most people use to refer to the woody part of the tree stem and not the leaves. Most of the soil minerals taken up by the tree are retained by the leaves and not by the bole or limbs of the tree, so leaving the leaves behind in the forest when tree branches and stems are removed minimizes the impact of biomass removal on forest soils, maintaining forest health and productivity for future generations.
Third, a number of states have established harvesting guidelines which will help protect forest health when harvesting for woody biomass. These guidelines include recommendations for avoiding or minimizing negative effects to the soil, the quality and soundness of any remaining trees and to the species and age composition of a remaining stand.