Because the effect puts them in a random order you don't get to stack your deck. If you have no sagas in the deck you effectively just shuffle the deck with no other game effects.

To add to the other comment, in general, you do as much as possible when resolving a card or effect.

The only exception is if something targets (specifically only with the word "target") and either there are no valid targets when it would go on the stack (in which case it cannot be cast/triggered/activated), or the targets all become invalid when it's time to resolve it (in which case you do nothing at all and just remove it from the stack).

So to answer your question, you reveal cards until you reveal a saga (which means you reveal every card in your library), then shuffle those cards back into your library.