Usually, a study of a prestressed problem includes using study steps. The first step is a Stationary step in which the static preload is applied. The preload step can be computed with or without taking geometric nonlinearity into account. In the second study step, where you compute the eigenfrequency or the frequency response, it is necessary to take geometric nonlinearity into account. Even if the displacements and strains are small, this is what gives the prestress contribution to the equations.
In a general nonlinear analysis, like a Stationary or
Time Dependent study step, the full combined effect of the prestress and other loads will automatically be included.