After having used a Lilligant extensively in-game and a Breloom extensively on PO, I strongly suspect that the belief that Sleep changed that way was only based on a poorly worded post (which meant to say that the victim will stay sleeping for 1-3 turns, i.e. wake up on turns 2-4). I've never, ever had a Pokemon wake up immediately after being put to sleep.
So long as you put the Pokemon to sleep after it takes its turn (or as it switches in), I do believe that you could theoretically juggle them until Dragon Tail/Circle Throw missed.
I think you didn't understand exactly what yoshiken said, when we talk about turn one is something like:
1-breloom used spore, random stuff fall sleep (in this turn it will never wake up, is what we call guaranted turn of sleep).
2-*
This is what we refer to turn 1* breloom did random stuff, the foe wake up.
That is what we call one-turn-wake up.
The biggest weaknesses to such a strategy is that nothing learns both Dragon Tail and Spore, and indeed the only Yawn users that learn it (as far as I can tell) are Blastoise and Slowking. Also, Dragon Tail only has a 90% hit rate, so unless you are using Zoom Lens (which I'm not even sure works when your opponent loses a turn to sleep), you're going to miss eventually. And there are more than a couple ways to work around sleep out there, not least of which is Sleep Talk (which I would imagine is fairly popular in Sleep Clause-less metagames).
Smeargle.
And the biggest weakness is actually that every shuffle move have a negative priority so with a turn-one wake the shuffler would:
1-die.
2-send out something that is wake up, ruining what the original asker wanted.
As a side note apparently there is some crazy shenanigans to overcome this: is by using assisted dragon tail (which loses the negative priority) and a sleep inducing move. I don't remember where i saw that, though.