You would still take the damage. The triggered abilities exist independant of their source and still resolve.
However, this gave me a cool idea:
Player A: I cast Manabarbs.
Player B: In response, I tap for 2 floating mana (no damage as barbs is not yet in play).
--Manabarbs resolves
Player A: I end my main phase
Player B: In response, I cast Celestial Purge (using the 2 floating mana)
--Purge resolves destroying the Barbs.