Is it possible to release the earthy citrus of a tomato in a soup without eating it? I have this idea that maybe along with other ingredients for a savory Thai-inspired soup that I can boil whole tomatoes with it to balance the savory flavor with the earthy citrus that the tomatoes have. But, the tomatoes themselves aren't something that should be eaten with the rest soup because actually biting into a ripe tomato is overwhelming and inconsistent with it. 

I haven't gotten much out of experimenting with it so far, so is there a way that I can just cook or boil the tomatoes with the soup so that it adds a the earthy citrus flavor but without being an eaten ingredient? I don't like the idea of canned tomato juice, I usually use fresh ingredients and it tastes more metallic.
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.