Search the web, or purchase a good strength of materials text for an understanding of fatigue failure. What I say below on the subject is very simplified.
The concept of "high cycle fatigue" is a generic consideration for any mechanical component that is subjected to repetitive loading/unloading cycles. The load might be reversed during a cycle; it might diminish to a lower value or completely to zero; it is necessary only for the magnitude of the load to change.
When this occurs in a mechanical component, the component might break, even if it is only subjected to loads that are a small fraction of the material's yield strength (or ultimate strength, as applicable). Fatigue failure is a rather complex phenomenon. What is relevant for your question is that fatigue failure is a "cumulative damage" phenomenon, and that it is a combination of the number of cycles, the magnitude of the average stress, and the magnitude of the cyclic component of stress. Lower stresses require more cycles till a failure occurs (on average). The number of cycles to failure can be related to total time of operation, and is referred to as the fatigue life of a component. (Much of this is probabilistic.)
Virtually all rotating components in a piece of turbomachinery, such as the compressor section of a gas turbine are subjected to load variations. Some of these load variations occur with a frequency once-per-revolution of the shaft. The gas turbine blades also see other load variations: because there are discrete blades - stationary and rotating - every blade experiences load variations due to the interruptions of flow and/or pressure caused by the nearby airfoils - upstream and downstream.
Compressor fouling is unlikely to change the frequency of any cyclic loadings; that is for the most part determined by gross geometry and operating conditions. However, it is possible that fouling will change (i.e. increase) the magnitude of the load variations, mostly by increasing flow disturbances, and in this way might reduce the fatigue life.
If compressor fouling is NOT uniform around the circumference of the turbine, for example local deposits on the inlet section due to non-uniformities of the entrance flow, this could result in a new cyclic load; possibly something for which the turbine design has not accounted for with regard to fatigue life. This might indeed be a serious problem.
