Theoretical question about Failure to Find and Tutor effects.

I was watching watching a video about [[Gifts Ungiven]] and how it can be used to only find 2 cards directly to the graveyard because it says to search for 4 cards with different names. This does not work for cards like [[Demonic Tutor]] because it says to search for Any card. This made me wonder if a card said “search your library for a card with mana value 0 or greater and add it to your hand”, which would encapsulate every single card in all of magic, could you still Failure to Find if the card had that restriction?