What is the "protégé effect," and does teaching actually help — even if the audience is imaginary?

Yes — Fiorella and Mayer (2013/2014) found students who studied AND taught beat study-only in 17 of 19 tests; Nestojko et al. (2014) found merely EXPECTING to teach improves recall, even if you never teach.

The protégé effect is the finding that preparing to teach, and teaching, improves your own learning. Fiorella and Mayer showed the teach-plus-study group won in 17 of 19 comparisons. Remarkably, Nestojko and colleagues found the benefit kicks in before any teaching happens: students merely told they'd have to teach later organized and recalled material better than those told they'd be tested — even when the teaching never occurred. The expectation changes how you process the material. This is why an imaginary student works.