You need to think it thru from a common sense point of view..
If it's an ATM fly and vol spikes huge,do you think the vol is implying the stock doesn't move,or makes a big move..which scenario benefits the atm fly?
If OP holds it to expiration, the only thing that matters is where the underlying ends up. If OP plans to exit prior to expiration, then volatility matters. Not just volatility but skew, term structure and the rest. OP can model the behavior of that particular butterfly by playing with IV, skew and term structure in BSM instead of asking us.
