I always attempt to bring the image to what the scene looked like with the naked eye when I was there. Basically, I’m wondering if I am capturing all the necessary data to achieve this in post processing when the histogram shows there is no clipping at either end. For example if the sky was a very saturated orange, is it necessary to add a shot that is exposed for the sky, or can I recover that color from my single shot in post processing since there was no clipping of the highlights?

Because of the way digital sensors work, if your main concern is preserving the highlights and your histogram shows no clipping there you are probably fairly safe that you don't need to bracket.

If, on the other hand, there are extensive dark areas in the image as well that you wish to boost in post, then bracketing for the shadows could be helpful. When we "see a scene with our eyes" our brains do a lot of compensation for different brightness levels in the scene and we perceive the darker areas to be brighter than they really are compared to the brightest parts of the scene.

Even when the histogram does not show clipping in the shadows, boosting the shadows in post will also boost noise, which is also above the clipping threshold. By taking bracketed shots that expose brighter to place the shadows closer to the mid-range tones, you will blow out the highlights but will preserve the details of the shadows with much less noise in them.