Can I beat a Pokemon Hardcore Nuzlocke challenge in Ultra Sun and Ultra Moon in a Randomizer Egglocke?

Nuzlocke Rules:
Fainted Pokemon must be permanently boxed
Only the first encounter on any given route may be caught (dupes clause)
All pokemon must be nicknamed

Hardcore Rules:
Always Set mode
No items from the bag option in battle (held items are ok)
No overleveling the next gym leader


#pokemon #nuzlocke #randomizer