Nope, the brightness and contrast dialog is its own thing. It has nothing to do with the individual colors, especially not HSL. However B&C is specifically an RGB effect only, and so if the color space isn’t RGB the colors are temporarily converted to RGB (via profile), the appropriate technique is applied, before being converted back again. Many of the photo/video effects in PS are exclusively RGB.
As I said, the legacy B&C works “naively” and you can very easily inspect what exactly it does if you turn on the Info palette and use the eye dropper to inspect the RGB values. Change the brightness and observe what happens to the colors. It literally applies the input offset to each of the channels, then clamps the result to prevent clipping.
The contrast is somewhat more involved, here are the two links explaining it more detail:
Brightness
Contrast
Photoshop never, NEVER, works with any of the colors in the HSL. It doesn’t have the HSL color space as a backing data model. HSL (or HSB as they call it) is only ever used in color pickers, because it’s more intuitive for the artists. The actual backing modes are Greyscale, RGB, Lab, CMYK, and Indexed (edit: Bitmap is Greyscale crunched to 2 bits, and I think Duotone and Multichannel are just variants of CMYK; both are used in the printing context anyway, with spot colors). Of these, Lab is the only one which has a bigger gamut than RGB (you obviously can’t experience this in practice, because our monitors are RGB anyway). There is also a 16-bit channel RGB (edit: and 32-bit), but this is intended for very specific uses in high-fidelity digital photography.
Finally, the modern (non-legacy) B&C behavior is much more complicated and much more aware of the actual image content, working in such away not to clip or “overburn” the image, which is actually extremely desirable when working with real photography, or else it becomes very easy to lose information, which is why a professional photographer would never touch the legacy B&C.
I am a technical artist and an ex-prepress guy. I look at all these from the point of data alone.