If Toofer said spell OR ability, I would say yes, Wall of Omens would trigger Toofer. Drawing a card is an enters trigger, so when when you cast and resolve Wall of Omens, you haven't drawn a card yet until after its enters trigger resolves.
But that only happens once the ETB resolved. Which is after the spell finished resolving & that's what Toofer actually cares about. So while WoO technically provides card advantage, it wouldn't trigger the guy's effect since they care about spells resolving, not triggered abilities.
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