Steve898,
If I understand your question correctly, you are describing the process of induction hardening the surface of a suitable steel (SAE 1035 and 1045 are frequently used in North America for this purpose) and then applying hard chromium plating by an electrodeposition process. The process is usually harden first, then chrome plate, then temper. The tempering operation also serves as an embrittlement relief (hydrogen embrittlement). 50 HRC on the surface is possible after low temperature tempering. This can be achieved through furnace tempering or induction tempering.
Now, to answer your question on the effect of chrome plating on UTS and fatigue, it is generally accepted that there is no reduction in tensile strength due to plating. The chrome plating is almost always polished to a very low surface roughness (~ Rz 1), which means that the surface condition is favorable. However, depending on the exact nature of the plating (thickness, type of deposit, presence of cracks), fatigue strength can be reduced. The best plating lines used today deposit a very uniform chrome layer, with many overlapping "platelets". So instead of depositing a single layer that has substantial residual tensile stress, and therefore will crack through its entire thickness, this rapid plating technology deposits a chrome layer that does not have substantial residual tensile stresses, and therefore its effect on fatigue is minimal.