You can absolutely tap your Birds of Paradise for mana in response to your opponent using Sudden Shock to kill it
Many players search for how many Uno cards are in a deck or how many Uno cards are in a pack when designing similar games
I imagine that, in the MTG universe, her magic in action would look something like the climax of Macbeth , or the Ents in JRR Tolkiens mythos
(Or something cheaper that already did its thing on arrival, and now is looking to die so you can return something bigger.)
(It's an artifact with ", Sacrifice this token: Add one mana of any color.") Whenever you sacrifice a Treasure, Captain Lannery Storm gets +1/+0 until end of turn
Then when you deal combat damage to player, you can pay mana to reanimate their stuff