This feature exists to ensure proper behavior when using Image Load Store or other incoherent memory writing.
To me, the part where it says, 'when using' seems fairly explicit.
"...this ensures that image load/store operations will only happen on fragments that pass the depth test."
I would say from what is written in that document that GL_ARB_conservative_depth is a filter for GL_ARB_shader_image_load_store.
It states that GL_ARB_conservative_depth is meant to prevent operations on GL_ARB_shader_image_load_store from being executed when the fragment fails the depth test.
I don't see anything that says they can be interchangeable replacements or substitutes for one another.