It might. The answer probably hinges on whether the cloudiness is organic or inorganic (mineral). Organic is usually harder because of biofilms and other types of fouling, some of which can even occur in visibly clear water. Silt or clay particles can be more easily filtered mechanically, while some organics call for chemical pretreatment (because they'll clog anything).

Unless you need the charcoal for taste and odor, simple mechanical prefiltration with mesh, cloth or paper filter media will give better flow and be lighter/simpler. Something as basic as a mesh bag stretched over your collection bag opening, or a coffee drip cone and paper/cloth filter.

Rafters on muddy rivers often use buckets to settle the water before treating/filtering. While it's possible to carry a collapsable bucket backpacking, it's still bulky and it takes time for water to settle, even with flocing chemicals. I've thought about it for glacier-fed rivers, but we're shy on those in California these days.