Awesome. It makes me feel all warm and fuzzy inside to know that the challenge is being attempted by someone. Thanks Mothrayas.
I know I said I had no plans to TAS it myself, but in order to watch Mothrayas's efforts I needed to get the tools, and as I had the tools I thought I would try recording a movie of myself playing. And I have good news, I don't know about the secret warp pipes, but the first world is completable.
One thing I noticed is that what buttons are being pressed on transitions (eg climbing onto the flying boss ship) can affect whether the game freezes or not, and thing done in one section can affect what you find in the next (I had trouble getting the boss to spawn). So maybe you can get to the secret toad house, but I don't think you can actually use any items, as pressing B on the overworld screen seems to subtly kill the game.
I have no idea how to upload my recording, but if anyone is interested in it, maybe give me a hint on how that is done.