Mark1 is talking about using the CC in a scene as a reference for WB. You asked about using it to make a camera profile for LR/ACR, which is a slightly different matter. My experience has been that the Adobe supplied profiles are generally quite good for general usage and if you are not demanding a high standard of color accuracy. {Editorial comment: My own feelings about color accuracy is that the chances are very good that I will be changing many colors. I don't see my camera as a scientific recording machine but rather as a portal to a creative space. That's for the arty stuff. For more mundane shots, my grandson doesn't give a eff if his jeans are exactly the right shade of blue, but God help me if my wife's new blue dress is slightly purplish.} But the Adobe profiles are made using just one or two units of a particular model and they may be generically valid but not spot on for every other unit in the world. So if your camera is far enough off the center of the bell-curve, it will benefit from profiling with the CC. Another point is that the Adobe profiles are dual-illuminant - they contain two profiles, one made under 6500K light and the other under 2800K lamps, and they are interpolated together in proportions that vary according to the ambient indicated by the WB. So for, say, 4000K light the profile values are a compromise. A home-made profile for that specific 4000K lamp and specific camera would, theoretically, be more accurate. This is especially true for weird illumination with a non-continuous spectrum, like LED lights.
In the LR/ACR internal workflow the profile comes first, correcting for the way the camera reacts to colors, and then the WB comes on top of that, correcting for the way the light has affected the colors. But the profile also contains a tone curve that adds another element - making it Standard, Neutral, Landscape, etc. However, since the derivative profiles are all based on the same basic lab measurements and the WB is supposed to be derived from external factors, it should not change when you change the Adobe profile. Going to a home-made profile might change the WB.
I guess the overall goal is that I want the colors to look exactly as they did to the eye and not like a de-saturated RAW image like it always looks like from my camera.
But your eye is different from my eye which is different from John Doe's eye. And if your color memory is like mine,... The best the profile can do is to aim for the CIELAB standard. But the profile is primarily about hue, saturation is a product of the added tone curve and the subsequent processing. If LR default processing isn't saturating enough for you, change it. It is easily done.