Yes it makes it harder.
For steels, the relationship between the minimum ultimate tensile strength and the Brinell hardness number is found to be Su=0.45Hb kpsi
from Mechanical Engineering Design by Shigley
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Case hardening increases the strength and hardness of the surface of the metal, which can lead to an increase in the tensile strength of the entire component. Member unclesyd recently posted some data on a certain alloy that was case hardened. Through hardening, meaning hardening through the entire cross-section, will definitely increase the strength, depending on a number of factors like austenitizing temperature, tempering temperature, etc.
As an interesting aside, automotive connecting rods are now being carburized (case hardened) for strength reasons. Typically, one would think of carburizing as a wear resistance measure.
Case hardening is normally applied to low carbon steels to produce a surface layer with a high carbon content. Then quenched from the normal case hardening temperatures a high surface hardness results, typically Rc60.
If the steel is a low carbon "mild" steel hardening of the core material hardly takes place. However the addition of assorted alloying elemments results in a steel those core can be hardened to a higher strength. Low carbon, low alloy steels are available for core hardnesses equivalent to 70/80 T/in2.
In general case hardening always hardens the core material because when you quench the case you can't avoid quenching the core.