Milton Friedman said yes, but on this question I am not convinced. Friedman thought the costs would be as high as 2.5 percent of gdp.
The standard argument is that a gold standard means more gold held in vaults. That’s less gold for tooth fillings or jewelry.
But the gold held in vaults involves an implicit option on conversion into jewelry. What is exactly the value of that option? Yikes, I feel confused after only a few sentences of this post.
But surely the real value of that option depends on the price level and also the division of gold into monetary and non-monetary uses. I therefore suspect there is some price level path where the option value on holding gold is equal, in risk-adjusted terms, to the returns on other assets. (A Mr. Smarty Pants TroubleMaker type might here cite Truman Bewley in response.) Probably that means deflation.
The gold in the vault is then no longer barren. It is no more barren than the gold held in your bureau, which is presumably an "option on wearing it to a fine dinner party."
The Friedman argument, to me, seems pre-Black-Scholes. Here are some related skeptical arguments.
That all said, I do not favor a gold standard. For behavioral wage-and-price-stickiness reasons I think mild inflation is better than a high probability of deflation.