How to approach research on an unproven theory for academic submission?
Lots of interesting things in science are not proven, so I don't think there's any special privilege for unproven theories vs. other types of subject.  The real question is this: what do you have to contribute to the intellectual discussion? It doesn't really matter whether you start from a perspective of aiming to prove, aiming to disprove, or just aiming to clarify (in fact, you might well change your perspective multiple times during your investigations). What really matters is that you will need to gather novel evidence that advances the state of knowledge with regards to the subject.