In the DLC yes, that's the purpose, you have to complete the story of this one to get back to the normal one. Alternatively you could play the original, which is an exclusively web game.
Viewing post in Let's Go Baby: Suffocation comments
But you disabled online for the original upload... so you're saying that now, you have to complete the expansion before you can play online in the base game's world?
Edit: Oh wait. I think what you're saying is you have to beat the base game to unlock the expansion campaign, and then have to beat that to return to the base game's world. Is that right?
To clarify. Let's go baby suffocation is a separate piece. It starts out under daddy's control. You have to complete the DLC for the world in the DLC to revert it back to its appearance in let's go baby friend's world. Suffocation and let's go baby friend's world are two separate things. Suffocation starts in the daddy-controlled world normally, let's go baby friend's world, does not.
Hope that helps