For the first time, Pokémon Mystery Dungeon Rescue Team DX includes Shiny Pokémon. These Pokémon will rarely appear in various dungeons as powerful bosses or in general and can require a lot of damage to be taken down. Normally they are just standard colours but you have a small chance of encountering them shiny. On the map, these Pokémon are marked with a yellow "Strong Foe" symbol
When taken down by your leader, there is a slim chance they will join you. However, if your leader has a Friend Bow equipped, there's a much greater chance they will join your team.
Only 27 Pokémon have the ability of being Shiny.
Source
Tl;Dr: Yes.
The list of Pokemon that can be shiny are
- Butterfree
- Ninetales
- Rapidash
- Electrode
- Exeggcute
- Exeggutor
- Starmie
- Magikarp
- Gyarados
- Ditto
- Dragonite
- Hoothoot
- Noctowl
- Ampharos
- Azumarill
- Sudowoodo
- Aipom
- Espeon
- Wobbuffet
- Shuckle
- Corsola
- Celebi
- Spinda
- Altaria
- Zangoose
- Metagross
- Ambipom
- Lickilicky
Hope this helps!
