I am doing an Egglocke. I captured a Phanpy in the route where you encounter Nora. I did not swap out the Phanpy for an egg before I began the Trainer School tournament. After the first of the three consecutive battles, the entire party is healed, as expected.
However, this included the Phanpy, which should normally not be usable while the Egglocke is in progress. I was then able to swap it out for an egg as usual after the end of the tournament.