Yes and No. There are two aspects of Auto.
Auto exposure (including Auto ISO, and camera modes A,S,P, and the Auto modes) give an automated exposure. Exposure affects raw images too. Can be auto or manual.
But all other settings (post processing after exposure), like Auto white balance, and contrast and settings like Vivid (which the Auto modes control, including Auto ISO - but the A,S,P modes don't, we can set them or not...), these camera settings do not affect the raw image. They are ignored by the raw data. These camera settings do still show in the Exif (as if they applied), and they do actually affect the embedded JPG that shows on the rear LCD, and which the histogram is shown from, but they do not affect the raw file data.
However, Nikon raw editors have the option to later apply the camera Exif settings to the raw file image, in the Nikon editor.
Other raw editors do not. Adobe raw can try to apply the white balance (from Exif, but temperature degrees K is not in the Exif), but no other of these settings can be applied. Note that the plan is that Raw software has its own settings to do this post processing, in the same way, but at that later time.
But later applying Exif settings from camera misses the point of Raw. If that's what we wanted, we could have just shot JPG. But the principle of Raw implies that we wait until we can see the image in the raw editor, and then we choose the best settings that will actually help it. We often have set the Exif settings a few months ago, and they have no particular relationship to the actual image in front of the camera.
Instead of guessing about the future picture we have not even seen, it is better to see the actual image first, and see what it needs, and see what actually helps it (one opinion).
We can (some of us can) always edit the JPG picture result to improve it, but a big point of raw is that raw can do it better, and easier. More range in the raw data, it comes out better. The raw tools are simply better (oriented to camera images instead of graphic images), and are much more convenient (we can set the same correct white balance in all of the batch pictures in one click, etc). And if raw, lossless edits apply, we don't have to overwrite previous bad tries, we always start from the original raw image in any subsequent edit. Raw has many advantages for those who actually care.