This experimental setup would only tell you whether this demographic (grad students or professors, or top performing college students) benefits from access to LLMs for acquiring a new knowledge or skill.
It would not prove that "the results depend on the operator". To prove this (and figure out the traits that make a proficient operator) you would either need a massive dataset to which you'd apply some machine learning to figure out the correlations, or at least you'd need a hypothesis on the traits you want to test.
Do left-handed people perform better with LLMs? Analytical thinkers? Dyslexic people?
It's not enough to just claim "some individuals will perform better with these tools" without any notion of who does, and whether it's possible to become one of these people, and what is the expected gain in this group.
Otherwise, sure, we could sell unsecured chainsaws as a tool for making ice sculptures and observe that "some people" are indeed more proficient at not getting their face cut off ; but if the tool is being marketed to schools, such a vague statement is not helpful in making a case for it.