Yes but in this case on top of the fee you stand to lose some money on the exchange rate. In this case there are two exchange rates, not just one.
I understand this is what happens if your money is in Euros and you bank in South America. The Euros get exchanged to USD, then to Pesos or whatever. It's one of the things that make living in South America less attractive if you hail from Europe as opposed to the US. I'm sure technically nothing prevents the banks to go from Euros straight into Pesos, it's just that the banks and the US SWIFT mafia want to maximise their cut.
It gets even worse if both these exchange rates are not the "good" Visa or Master interbank rates but some less good rates invented by the bank.
Long live crypto!