The thing is, while the universe is full of metals, it's not that full of the materials needed to sustain life (as we know it, at least). You can find metals and other inorganic compounds on virtually every asteroid, moon, and planet, and many comets even. But water and nitrogen and carbon are significantly rarer.
Plus, life can't survive more than a few minutes in space without metal encasings and electronic life support; whereas metal alone only requires life at a much longer time scale. So, while it may be possible to build a fully inorganic self-replicating fleet, it's certainly impossible to build a fully-organic one with any technology or chemistry we know about today at least.