Something would happen. I'm not surprised what I'm about to write has escaped some experienced players. There's never a need to look this up, so it's more of a Pokemon trivia fact.... Only in Generation 1, if the Pokemon Pikachu is deposited in the Pokemon Storage System, then Pikachu will lose 1 redeemable friendship point from it's current friendship value. It is a myth that friendship calculations did not exist in Gen 1. The Pokemon Pikachu (and ONLY Pikachu) had a friendship calculation even in Gen 1. After Gen 1, the Pokemkon Storage System stopped influencing friendship. It is also worth noting that the friendship deducted is not base friendship, which is very complicated in earlier games.
So yeah, the answer is sort of confusing if you're reading this with little Pokemon knowledge. Basically all this means from a practical standpoint is that it's a bad idea to put Pikachu in the PC, then remove it, then put in the PC again, and so on just for fun. It's OK to put Pikachu in the PC whenever you want to make room for another Pokemon, and you won't lose Pikachu or anything. The answer isn't supposed to scare you into keeping Pikachu in your team forever. Friendship is an almost useless calculation in Gen 1 anyway.