There are no savings given the volatility. Since it can take days to convert to usable currency, you'd have to bake in 3-20% padding to cover volatility.
All payment processors take currency risk. Coinbase has an interesting approach by also being an exchange and doing some algorithmic arbitrage.
The current volatility isn't inherent to the protocol, it's just a function of market depth and liquidity which will presumably improve/stabilize as the network grows.
Exchanging into dollars is momentary, it's dollar withdrawal that takes days. So, actually the only risk that's being taken by bitpay is the fifteen minutes between the moment the price is displayed and someone pays (after 15 minutes the proce they lost in btc becomes invalid)
And even against that risk they can hedge. So it can really be sustaining.