Plug-and-Play methods for image restoration are iterative algorithms that solve a variational problem to recover a clean image from a degraded observation. These algorithms are known to be flexible to changes of degradation and to perform state-of-the-art restoration. Recently, significant efforts have been made to explore new stochastic algorithms based on the Plug-and-Play or REgularization by Denoising (RED) frameworks, such as SNORE, which is a convergent stochastic gradient descent algorithm. A variant of this algorithm, named SNORE Prox, reaches state-of-the-art performances, especially for inpainting tasks. However, the convergence of SNORE Prox, that can be seen as a stochastic proximal gradient descent, has not been analyzed so far. In this paper, we prove the convergence of SNORE Prox under non convex assumptions.