Very cool idea. I think you could make a case for this based on the inherent dependency that some life has on other life. It depends on how large a system you want to look at.
Our cells have organelles called mitochondria which let us convert food into a form of chemical energy that is directly usable within cells. Mitochondria were almost certainly there own species of proto-bacteria that were taken up into eukaryotic cells far back in the evolutionary process. To this day, mitochondria still have their own DNA and replicate themselves independently within our cells. Without them, we'd die within the day.
Can you see ecosystems in a similar light? Bacteria that fix nitrogen gas in the soil are necessary for plants to grow. Plants are necessary for oxygen-dependent animal life to function. Prey animals will reproduce too quickly and decimate their habitats without predators to regulate their numbers.
You could analogize the entire earth as a sort of "cell" or "organism," which individual organisms making up the analogues to the "organelles" or "organs" that work in synchronicity to keep the whole going. I'd say the earth is a bit more robust and actually less interdependent than the organ systems of our body; it can evolve life and spring back even from mass-extinction events. Still, a neat analogy.
I think I see it less in terms of interdependency or of the earth as a cell. The earth I would clearly demarcate as environment separate from entity.
If 'Earth Life' or 'The Entity' began as a single cell with a prime directive to exist and survive, and to do so it employs the mechanisms of adaptation and reproduction, then all subsequent expressions of this original entity are still the entity. All past and current expressions are the uninterrupted continuation of its existence or survival. Some parts of the Entity may be interdependent as you describe, but all of the entity does not have to be. It all depends on what is required to adapt to different or changing environments, to be maximally resilient by exploiting any possible resource in any manner possible. All that matters is that any expression continue to exist, not any particular expression.