Hello DurhamLad, and welcome to the friendly Camera Labs forum!
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Now I assume you have to decide between processing the images in a way that you are satisfied or that other people are. Is that so?
As to your Q relating to dark and/or overcast light. If you mean light that produces dull colors then you're right: HDR can map brightness values to colors in a way that the results looks more colorful than the unprocessed image. But it need not be so. There are many ways to tone-map and some people try to avoid the overly colorful look. So it depends.
If you look at shoots that are taken in very low light these mostly have very high contrast as some parts of the image lie in total shadow whereas some other parts are probably shone on by some street light or other light-source. In those cases HDRing the image can compress the extreme dynamic range of the original and produce an image where you can discere details in the darkest shadows and
details under the light. But this does not necessarily mean you get some "boosted" colors.