Relic Castle

This is probably a stupid question, but im rather new to the whole fan game thing.
So, I'm putting a plan together for a pokemon fan game that I'd like to make, and I was wondering if it would be possible to make a unique version of an already existing pokemon.
For example, let's use pikachu. (I'm not going to use pikachu, but still).
I'd like pikachu to exist as a wild pokemon, with no real changes from other games, but I'd like to also give the player a special pikachu with a unique sprite, stats, movepool, etc as well as making it impossible to release into the wild.

Is this possible? And, if so, how difficult would this be to implement?

Would it just be easier to implement as a separate pokemon entirely (as far as the game is concerned)?
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