The HAZ or "white layer" that is produced on the exposed surface of the part when wire EDM is performed usually runs between about 0.0002" to 0.0005" in thickness. This thin layer of material is re-austenitized by the EDM process, and it is very brittle. This makes it is an ideal initiation site for cracks. Once cracks form in this thin layer, they can then propagate into the base material, and ultimately lead to the failure of the part. So the anticipated effect would be a measurable reduction in the fatigue life. In order to quantify the effect you would need to measure it by performing fatigue tests using your material, given your specific geometry and loading conditions.
There are two practical ways to combat the effects of the EDM white layer. The method that you choose will depend upon the material in question and the limitations of your design. As suggested above, a final grind of the part after EDM will remove the white layer, and eliminate the problem. Another method that is commonly used on hardened high speed and tool steel parts that cannot be surface ground after EDM is to stress relieve the parts. This usually amounts to tempering back the white layer to give it some amount of ductility. As long as a suitable temperature is selected, it should not significantly reduce the hardness of the part.
What material are you using, and at what hardness? This information may allow us to provide you with some more detailed recommendations.
Maui