To a certain extent, they do, at least for farmland. Studies in Europe have shown that many vertebrate, insect, and plant species of farmland have declined in parallel. In contrast, only a few species have increased, and these changes are thought to be driven by agricultural intensification and specialization (see table 5 in Gregory et al., 2005). So it is reasonable to assume that trends in bird populations mirror those in other taxa, at least in farmland.
On the other hand, no single metric is likely to describe changes in biodiversity as a whole adequately, and the bird trends cannot be straightforwardly generalized to biodiversity. PECBMS recommends further work to explore the correspondence of across-taxa trends and encourages the production of some other indicators as well, such as the butterfly indicator that has already been produced (see more on the EEA website).