Well, not quite what you are asking but, it has been shown that asking some demographic questions prior to testing can alter some outcomes (specifically Black students' math scores) [0] although other papers find no difference when looking at other factors such as asking about gender prior to physics tests [1], this is known collectively as "Stereotype Threat."
So given that "Stereotype Threat" is a thing, I would absolutely believe that you can apply the placebo effect to learning as well.
I would kind of start to think about formative vs summarize questions but unrelated questions you get right could
Until I can find the link to the study, anecdotally I have found that sharing a message about adult learning prior to learning can also have have a positive effect - which sounds similar to the above.
So given that "Stereotype Threat" is a thing, I would absolutely believe that you can apply the placebo effect to learning as well.
[0] https://onlinelibrary.wiley.com/doi/full/10.1002/ets2.12046
[1] https://arxiv.org/ftp/arxiv/papers/1602/1602.07648.pdf