Technically, the Motion Path is not a "shape outline", it is the representation of the animation an object will follow. It will change under any other influence. I will attempt to explain:
In the image below, you see a faded light gray outline. That is a Bezier object that I used as a Motion Path Geometry shape (make sure Attach to Shape is checked)... it's one you can actually see and one that doesn't change as you make modifications to the actual Motion Path behavior.
The dashed red and black line IS the Motion Path. It is distorted from the original geometry shape due to the 3D Parallax you always get in Motion. Therefore, the right side of the Motion Path is closer to you / it's elevation is raised in Z-space. Now take a look at the GIF below.


This is the scene rotated (via camera / Rotation > X -72º).
The change in Motion Path is due to a Custom Behavior with Position > All added as well as Rotation > All added. Increasing Custom > Position > Z bends the Motion Path by elevation. You can control the "fineness" of this shape by keyframing and using Bezier control points.
I did *not* go through a lot of trouble to make this demo. However, using Custom > Rotation angles, I can animate things like the roll, pitch and yaw of the airplane model (also not an easy task - it takes practice to know how to make it all work.) I will say, it is so much easier to "mold" a Motion Path by adding to it rather than trying to manually distort the shape in the Canvas.
Be careful using 3D Models. In all likelihood, you will have to go into the 3D Object inspector and change the orientation so that it will actually follow a Motion Path with a Snap Alignment to Motion behavior. For this Airplaine.usdz, I had to set X to -90º and Y to 180º.
All that said -- you gave me an idea of using a duplicate Object + Motion Path I hadn't tried before. It looks like this:

I'll go into the details later — the explanation may be a little lengthy and I don't want to confuse you with an alternate set of details (just goes to show you: there's usually more than one way to do things in Motion!) I also have a ton of other things I have to do for awhile before I can get back... :P