Is it possible to release the earthy citrus of a tomato in a soup without eating it?
Yes, it’s doable, but you will have to plan for an extra step and possibly few hours of preparation before you can start with your actual recipe:

The haute cuisine approach: 

Make a clear tomato soup (sometimes also described as “essence” or “consommé”) and use this as an ingredient in your soup.

There are cooked and raw methods and both rely on separating the tomato (and other ingredients) from the liquid, either by very careful straining through a cloth or by an egg white raft.

Or simplified:  

In a similar process, you can simply cook the tomato in the liquid you are going to use for your soup, strain out the solid tomato bits so that just the purée gets into the liquid and continue from there.

Even simpler:

Use a stick blender for the soup base in the previous step.

Note that the consistency and opaqueness will change depending on the method you choose, from thin to thick, from clear to opaque and the same goes for the flavor profile.