The Pigou effect is that a lower price level increases real money balances, real wealth, and consumption. It applies to outside money, and not inside money.
In a previous post, I argued that inflation targeting combined with Ricardian Equivalence means that there is no Pigou effect. Inflation targeting makes base money into a type of inside money--fundamentally a type of government debt. Ricardian Equivalence implies that while a lower price level raises the wealth of of those holding base money, it increases real tax liabilities. There is no net effect on real wealth, and so no increase in real consumption.
For many years, the Fed almost entirely held government bonds. But recently, the Fed has shifted to holding a large amount of mortgaged-backed securities. If the price level is lower, then this increases the real wealth of those holding base money, but it reduces the real wealth of the indebted homeowners. To a large degree, there is no longer a Pigou effect for a substantial portion of base money, even without Ricardian Equivalence.
Further, 100% gold reserve banking would substantially increase the proportion of total wealth that is "outside" money. Such a monetary regime would have a much stronger Pigou effect. That is, even if nominal interest rates couldn't fall, say because they were already zero, then a lower price level would have a relatively larger effect on real wealth. The decrease in saving supply, increase in the natural interest rate, and increase in real consumption would be larger. In other words, a smaller decrease in prices and wages would be necessary to bring real expenditure in line with capacity.