Certainly, unskilled workers constitute the bulk of the working population of any pre-industrial society. So their wages would provide information regarding overall productivity. Slavery didn't reduce the wages of unskilled workers directly, they would only do that if the existence of slavery inflated the supply of unskilled labor relative to skilled labor, if slavery didn't exist (i.e. if many slaves wouldn't become unskilled laborers), but that's improbable as the vast majority of workers were unskilled workers.
The bulk of the population was rural (maybe 80% or more) and I don't believe peasants can be called unskilled workers especially because they were rarely wage workers in preindustrial societies. They can more easily be described as tenants, small landowners, people with rights on community lands, long term skilled employees and a myriad other relations that created a very complicated rural system of land and labor relations before capitalism. Probably the only unskilled workers employed in farming were those used for occasional, larger projects or for seasonal work like harvest when the usual resources of labor were insufficient.
The study exemplifies unskilled workers as " i.e. farm labourers, camel and mule drivers, water carriers, and sewer cleaners". With the exception of the farm laborers I mentioned above the other categories don't look large enough to have an impact.
Slavery can reduce the price of labor because removes choice (for example many freeman could refuse to do a work like sewer cleaning pushing the wage up but a slave can be forced to do it) and because they can be kept at a subsistence minimum. Of course this must be correlated with the price of slaves and the ability to control them.
The bulk of farm laborers were unskilled workers, because they didn't have much human capital invested. What is human capital? A skilled worker may know how to read, a unskilled don't. Human capital is the capital invested in education and courses. Workers would be skilled or not depending on their human capital invested. If they are wage laborers or tenants or small landholders, it doesn't matter according to this definition. They are workers as long as they are a part of the workforce, they don't need to be a part of the labor market.
Reading did not had much to do with the practical professional skills that were transmitted through generations or apprenticeship. A peasant needed and had the skills to grow plants, raise livestock, do home industry etc. Even if they did not get a diploma they had some informal education. The level of skill of peasants has always been (and still is in areas where agriculture is not industrialized) a key factor in rural output. Not anybody can be a succesful peasant, one needs an investment in human capital for that, otherwise he can be used only for digging ditches or picking fruit.
The graph that shows romans had 10 times the number of shipwrecks than the Mediterranean at the hight of the Italian merchant republics is shocking. Either they were the worst sailors ever or we have no idea on the scale of shipping they did.