I wonder depends on the material and how much robust and reliable you want the outcomes. What I've seen is that non-linear damage models are common when you have a variety on loading conditions for linear homogeneous and "isotropic" materials (commonly on steels), or when the anisotropy of the material is quite relevant. If you don't present one of those scenarios, you should be set with the linear theory, at least to get a rough result.

Depending on the application and on the anticipated failure mode for the problem that you are studying. It is good to run both for similar conditions first to see any major difference. Also it depends on the anticipated fatigue stress range, whether it remains below the elastic limit or not.