Yeah, if you saved over all three files on the game, and you had already gotten New Game +, it'll still be there.

What I had done was accidentally delete all the files and took off New Game + and such, but I didn't mean to and had to start completely from scratch.

Since you already have New Game + on your cartridge, it doesn't matter how you beat the game since regardless, you have New Game +.

I'm talking about if the only option was New Game and you had to start from scratch.