TL;DR: It's acceptable, but I would get a second opinion.
I've never heard of anyone using the phrase "their very self", but I have seen "very existence", "very soul", etc. It's simply a tool for emphasis, so using it to emphasize an important point in any writing (academic or creative) doesn't seem out of place to me.
However, I don't spend much of my time writing academic and technical essays, so I wouldn't say I'm an expert on academic vernacular. I recommend you have someone read over the sentence in the context of the paper, and if they have no problem with it or don't even mention it, you're in the clear.