No, your distribution is the distribution. Your distribution doesn't make Linux from Scratch into one. Let's say I think your distribution is the best one for me. That does not mean another distribution created with the help of the documentation found at Linux from Scratch the best one too. Those are two different distributions. Linux from Scratch remains the documentation how to create one.

It's like finding a video tutorial how to program your own program a little game. The video tutorial doesn't become a game, it remains documentation how you write your own game. That's comparable situation with Linux from Scratch (in relation to our discussion).