Do you need the base game for Mario Kart 8 Deluxe Booster Course Pass?
Yes. Mario Kart 8 Deluxe Booster Course Pass is extra content and only works if Mario Kart 8 Deluxe is already on the same account and the same platform. Without the base game you can redeem the code but play nothing.
Same account, same platform
Buy the DLC for the platform where you already own Mario Kart 8 Deluxe. Redeeming it on another account or console makes the content unusable, and that cannot be reversed.