Is "cell proper" considered a biology term / well defined concept?
This isn't a special biology term, it's just an English usage thing. "The X proper" just means "the X, strictly speaking". As well as the question you quote, see also this question on ELU.SE. I would expect this use to be understood by many biologists who speak English as a first language, but there are certainly clearer ways of saying it.

Regarding this particular example, the author appears to be proposing a way of defining a vacuolated plant cell. It sounds like he is proposing a definition that excludes the cell wall, but he confusingly calls the cell wall the "(cellulose-)membrane" (the 'primordial utricle' is the cytoplasm, I think). However, I am afraid I am not an expert in the history of plant cell biology and can't really comment on whether it is a useful contribution to, or synthesis of, the state of knowledge at the time.