It would still exist if it was missing one of the three, but it wouldn't be alive. A soul combined with a body but lacking thalergy is what we call a revenant.

[Ianthe paused in thought, thinking of how to phrase things.]

The whole is more than the sum of is parts. It's only when combined together do those matter. Like the human body. It's only flesh, blood, and bone. Individually they are nothing but tools and resources. Combined they create something capable of holding a soul, capable of being infuses with thalergy.

It's ok that our people have different views on what constitutes life. They're close enough, and I've dealt with planetary souls before.