My phosphate level was over 5,000 for several years without any issues at all. CC was always zero. Chlorine usage was normal. Phosphates does nothing directly to increase CC, though as Bama mentioned it can have an indirect effect by speeding up the growth of algae.
swimcmp, situations like the one you report typically come from failing to understand how the shock process works and thus never killing off the algae growing in the pool. If you shock as described in Pool School, it really doesn't make any difference what your phosphate level is. Off course, it is possible to kill off the algae in other ways, for example by lowering the phosphate level, but that ends up being more expensive and more likely to cause other problems.