In answer to your question on whether an Earth scientist primarily studies the geosphere, we can break your question down into two parts.
An Earth scientists job is to study the earth's entire atmosphere, primarily the layers embedded within it, including the crust, the core, the mantle, the outer core and inner core.
What earth scientists study
There are also three types of rock which are of predominant concern to an Earth Scientist, which are Metamorphic, Igneous and Sedimentary rocks.
The geosphere refers to the solid part of the earth, consisting of the crust and outer mantle. It is also is the collective name for the lithosphere, the hydrosphere, the cryosphere, and the atmosphere. It is usually concerned with the upper most layers of the solid Earth.
So in answer to your question, yes, an Earth scientist certainly studies the geosphere, but the Earth consists of 5 layers, of which an Earth Scientist would be concerned with it's entirety, and not purely isolating the upper solid layers.
