Setting aside the money relation, whether or not goods become more or less scarce (and therefore, command higher prices or lower prices) would be determined by whether or not the additional persons in a growing population produced less than or more than they consumed.
If they are duplicating the existing production processes, then, they will be producing more than they are consuming. But, in that case, goods are becoming less scarce and their prices would be falling.
If they are producing less than they are consuming, but their deficit is being made up by reduced consumption of the existing population, then the scarcity of goods is not changing and prices would stay the same. Only in this case could the population actually increase while the additional people are producing less than they are consuming.
If they are producing less than they are consuming and the existing population does not distribute goods to them, then they will die and population will not increase and scarcity and prices will not change.
It seems to me that historical cases of rising population, at least in the market economies of the western world, correspond to the first case.