Yes—usually, if the file preserves that metadata.

If you shoot RAW, the Auto White Balance setting chosen by the camera can typically be viewed in Lightroom or Adobe Camera Raw, where the image will show white balance as temperature and tint values.

If you shoot JPEG, those values may still be embedded in the file metadata. One way mentioned is to open the file in Photoshop, go to File Info, then Raw Data, copy that text into a text editor, and search for entries like “temperature” and “tint.”

Keep in mind that these values are metadata used by software and may not always map perfectly to a simple in-camera Kelvin number the same way a manual setting does, especially across different camera brands and software. But in general, yes: with RAW files in particular, you can usually recover the camera’s AWB result as temperature and tint.