It would be possible, but it would also be just about the hardest way to go about doing it. Not only would there be next to no interactivity (no real-time feedback on the image changes) while you create your gradient, you need to mentally manage the translation between the RGB 0-255 scale that the info panel displays and the 0-100% scale that the gradient editor uses. Curves would be a lot easier to use for basic contrast adjustments, and even for things like creating a Sabattier effect.

The Gradient Map comes into its own when you want to do things like creating false colour (which can include toning black and white images to imitate darkroom toning, alternative processes or aging effects), or when you want to unify colour gradations in your image (particularly, but not exclusively, skin tones, which often vary wildly between face, hands, arms and "everything else"). In those cases, the concern is "when the underlying image is about this bright, I want it to be about this colour", and an appropriate choice of blend mode and opacity (along with masking) can make the desired effect easier to achieve than playing with individual colour channels using Curves or Levels.