The Poké Ball (Monster Ball (モンスターボール Monsutābōru?) in original Japanese language versions) is a spherical device used by Pokémon Trainers to capture wild Pokémon and store them when not active
So the answer is no, because when a Pokemon is returned to the Poke Ball, it's not active.
Another scenario is when traded Pokemon evolve, but only when they are called out of their Poke Balls after the trade as happened, e.g. when Bianca & Prof. Juniper traded Shelmet & Karrablast, meaning that they do not evolve in their Poke Balls because it keeps them in a stat of inactivity.