There's some evidence now that viral load peaks in the first week, and it's the second week that tends to be a problem for people with very serious cases. By the time many of these patients are hospitalized, their viral load is already going down on its own, and their serious complications are either due to immune overreaction (the so-called "cytokine storm"), or some sort of opportunistic co-infection like bacterial pneumonia.
It's decently likely from what I've been reading that there might end up being effective pharmaceuticals for each stage, but that they'll be totally different from one another: maybe HCQ and antivirals like remdesivir or favipiravir early, and maybe immune-modulators like tocilizumab or even corticosteroids in this second phase. But again, the devil will be in the details, as it looks like HCQ doesn't work late, and steroids or other immune modulators might be actively harmful in that first stage when the virus is still surging.
As for mechanism: nobody is really sure. HCQ does have some immune-modulating effects (that's what makes it useful for lupus), but there's also speculation that it might have some effect on the interaction between the ACE2 receptor and the coronavirus spike protein, and so somehow inhibit viral entry (see, e.g., https://www.nature.com/articles/s41421-020-0156-0).