Rotate game object and its rigid body independently of each other?

The transform of a game object is what describes an object in 3D space. Every game object and every component must be linked to a transform or else it can't exist in the scene. To reiterate: all a transform really is is the description of where an object is in the scene.

In terms of your question the answer is a resounding no: you cannot separate components from their attached game object, nor can you separate a game object from its transform. That being said, the way that you separate various components from each other is to use child objects. That way you can have the audio listener at a robot's head, and locomotion scripts attached to its feet, and a laser script attached to its gun, etc.

What you're asking sounds very strange to me. It's like asking "can I detach a person's gravity from their body?" What is it that you're trying to do, and why don't you think you can do it in Unity's current framework?