I am going to provide a spectrum of answers, as parts of your question can be interpreted in very different ways.
First, in the title, you ask about getting a degree "without having been a doctoral student". But what exactly constitutes "being a doctoral student" here?
Is it about being enrolled as a doctoral student? In that case, the answer is very much yes, as some universities have no formal requirement to enrol at all while you work toward your doctoral degree. You may well be employed there as a research assistant by the department where you work on your doctoral research, but whether you also enrol as a student during that time may be unrelated, irrelevant to your department, and based on totally tangential criteria (e.g. whether you need the public transportation ticket that comes with enrolment).
Or does it mean having an (at least informal) agreement with a possible supervisor that you are working on research that is supposed to bring you a doctoral degree? That is indeed adviseable, though it is not totally inconceivable that you may be working on some research questions without any such clear goal, and only later on manage to assemble all of them under a common topic that happens to be of sufficient interest to a professor so they agree to supervise you on the "last few meters" until your defense.
This means, however, that you need to get much of the input on procedures and customs in research from elsewhere, preferrably by already being embedded in a group of researchers beforehand. For, even though you may already have the right ideas on what to investigate, it is this operational knowledge - what is a paper and how do you write one, how and where do you publish it, what should be included, etc. - that you (have to) pick up while working toward the doctoral degree. And this does not even touch upon having non-paywalled access to the relevant literature.
Thus, without being embedded in a research environment at all, the answer is rather no.
In the question body, you then ask "whether it is really possible for John (...) to promote his personal work to obtain the title of doctorate or at least to pursue his personal project as a doctoral research project with an approved organisation".
Here again, I'd say the answers is generally yes - ideally, your research project for the doctoral thesis (or projects, as there is often not just one singular "thing" to look at) should kind of be your personal project, in the sense that it is something you came up with and defined, possibly built yourself in part or in full. Again, you need to know what you are doing research-wise, so creating a project (and using it in a way that produces results relevant for research1) before having any exposure to a research environment and its conventions is not impossible, but very unlikely.
1: i.e. running user studies, doing software benchmarks, analyzing data sets, depending on whether the project is the research topic, or is a tool that allows you to gain new insights on the research topic.