Can Elnuk Herd focus himself?

Yes — if "focus himself" means his own "when you play me" effect targeting Elnuk Herd himself, that works. "Focus" isn't something a unit has (Focus is the permission a player gets during a Showdown, Rule 313), but Elnuk's play effect reads "give a friendly unit +3 might this turn," and he is a friendly unit.

If played from hand, he simply gets +3 Might this turn and stays at the battlefield. If played from face down, the Hidden targeting restriction (811.1.d.3) still allows him — he's at the battlefield he was played to — but then his own "recycle me" clause sends him to the bottom of your Main Deck right after, so the +3 on himself accomplishes nothing (he's gone, and the buff doesn't follow him). Better to aim the +3 at another friendly unit at that battlefield.