Almost always, no. The may have "no fees" but they chose the exchange rate.Wouldn't it be cheapest to do a bank to bank transfer?
I noticed when I used to convert money from pounds to dollars, some banks have agreements with other banks in other countries that will give a discount on transaction fees. It might be worth seeing if there is a similar case in this situation.
pretty sure the post office would give u a better rate than a bank unless your a special customer