Potentially, yes. During the Great Depression, Hoover and FDR attempted to go the opposite route. They forced industry to keep wages high in an attempt to end the financial chaos. When FDR attempted to pull back on New Deal programs, it became apparent that the inflated wages were not enough to keep the depression at bay.
Of course, we were overproducing leading up to the depression while earning low wages. This simply led to using credit to overspend.
What you are describing is how classical economists say an economy will respond to a recession.
When a recession happens, there will be (in the short term) too many workers. So some of them will get laid off and wages will drop as well. As you say, when wages drop, employers will be able to hire more people to work. When they hire more people to work, supply goes up. This supply creates its own demand because the people who are hired can buy up the increased output that you mentioned.
So yes, you are correct about the mechanism.
The total output of a good produced and sold in an economy is dependent on many factors. Fall in wages for a product only affects the manufacturing cost of a product, which causes its supply curve to shift to right. In other words, the producers will be willing to supply more quantities of the product for the same market price. As per this analysis drop in wages would result in increase in quantity of that product supplied. However, there are many flaws in the logic.
First we have considered only one product in our analysis, whereas there are many different products in economy, and if wages fall for all the products than we will need to consider impact of other products also. Second flaw of the logic, and this is the more important part, is that we have considered only the supply curve. We have not considered the impact of fall in wages on the demand curve. Reality is that fall in wages, directly impact the total disposable income of the consumers. This tends to shift the demand curve to the left. That is the buyers are likely to buy less of a product for the same market price.
Thus in general we can say that fall in wages will not necessarily result in net increase in production. To know exactly what will happen, We will need to understand the impact of fall in wages on demand as well as supply curve. Also we will need to consider the relationship between the demand for different products.