Yes. There have been published efforts to reverse-engineer or approximate manufacturers’ in-camera JPEG processing.

Examples mentioned in the community answers include:

• Darktable-related work summarizing projects in this area.
• Pascal’s ColorMatch, which builds ICC profiles from out-of-camera JPEGs photographed against a known color target.
• Guillermo Luijk’s work, including reverse engineering of RGB curves.

In practice, people usually reverse-engineer parts of the JPEG pipeline—such as tone curves, color rendering, and profile behavior—rather than perfectly reproducing every internal step a camera uses. That’s because different makers apply their own combinations of demosaicing, color transforms, white balance, sharpening, contrast, saturation, and noise reduction.

So the short answer is: yes, this has been done to some extent, and there are public projects and articles documenting it, especially around color profiles and tone/RGB curve reconstruction.