If I play a spell from hidden that has a replacement effect, does that effect apply to damage from a 'when you play a card from face down' triggered ability?

Ruling: Yes. When you play a card from hidden, the card fully resolves before any "when you play" triggered abilities are placed on the chain. If the played card creates a replacement effect (like Lotus Trap doubling damage), that effect will be active when the triggered ability resolves.

Sequence:

• You play the spell from hidden and it goes on the chain
• The spell resolves and its replacement effect becomes active
• After the spell has fully resolved, "when you play" triggered abilities (like Katarina, Reckless's ability) are placed on the chain
• When those triggered abilities resolve, they are affected by any active replacement effects from the card you played