If you shoot in Raw, that camera setting is irrelevant because it applies only to jpgs made by the camera. Raw files are greyscale data files and therefore have no color and no color space. The color is created by Lightroom. At the time of outputting a rendered RGB image, either with Export or Edit In..., you choose the color space in which it will be rendered.
If, OTOH, you are editing jpgs in Lightroom, you could increase the saturation and thus create new (artificial) colors in the image that are beyond the gamut of the original jpg's space. Saving the new jpg in ProPhoto RGB would preserve those colors.
BTW, a smaller gamut does not mean "less info". It means the same amount of data refers to a narrower range of colors.