Hi Shawn,
Yes, any object visible from the camera will show the world's position.
You want to move the camera, which will stabilize this information on non-animated objects.
What you need to make the particles invisible is the data that is not shown, the "Viewing Shadow."
While the camera moves, the parts of an object that is visible to the camera change. You can calculate the distance between the camera and the Object. Since you don't get the particle's position, you get nothing more than a 2D idea of the camera-object relation.
Let's say you have that particle position; you would be able to obscure all the particles behind objects, but what about particles that would bounce into objects, like the front round part of the cylinder? Where do the particles go when they become invisible, through the Object, and then become visible again later? Typically, they bounce, which needs complete information on all parts.
Is that creating a more precise "picture" of the problem?
Cheers