Regarding the Project Core

Well, I might've just been a bit dumb, but when reading the description I thought the project cores were meant only to give the cool looking champion loading screen thing, but then when I traded in my project cores for the Master Yi Project Blue Print, I received the skin shard which I have already... So I was wondering, if I had used the project core for, lets say, Katarina's, then would I have gotten her project skin? I feel like I just made the mistake of my League of Legends life. -_-