Can you play Nocturne, Horrifying even if you draw the looked at cards?

Yes — drawing the cards you looked at doesn't stop you from playing Nocturne.

That restriction was in Nocturne's old printed text ("...and don't draw them"). The 2025-10-21 errata replaced it with "As you look at or reveal me from the top of your deck, you may banish me. If you do, you may play me for [A]" — so the trigger is the look or reveal itself, which happens before any draw decision. Whether the effect then draws one of those cards (or all of them) is irrelevant, because you already banished him out of the looked set.

He finalizes onto the board once the whole effect that revealed him finishes resolving, so he doesn't interrupt the rest of the look/draw (FAQ #13168). And no one gets a Reaction window mid-resolution before he lands (FAQ #12292).