Can I beat a Pokemon Randomizer Hardcore Nuzlocke challenge in Infinite Fusion?

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 #infinitefusion