Yes. You just need to complete the main game first before you can evolve, and that goes for every Mystery Dungeon series so far. For Gates to Infinity, you evolve after your main character Pokemon has returned from the human world, then after a few more requests, you evolve by what your Pokemon would usually do to evolve (e.g. level up in a dungeon or exposure to a certain item etc.).
Bulbapedia - PMD: Gates to Infinity
