Since the total entropy of the universe is increasing because of spontaneous processes, black holes form because of entropy (correct me if I'm wrong), and the universe is always expanding, would the universe be consumed by black holes or would its area increase too quickly for that to happen?
Entropy isn't a force that causes things to happen.
But anyway, the answer is no. Not all matter in the universe is expected to eventually collapse into black holes. See Adams and Laughlin, http://arxiv.org/abs/astro-ph/9701131 , section VD.
Note also that black holes eventually evaporate, so when matter collapses into black holes, the result is that it eventually gets recycled into Hawking radiation, most of which is photons.