Only as a partial evidence, as it’s possible that 1) model is overfitting, 2) posterior predictive check is misleading, e.g. 2a) if kernel density estimate is used it can hide problems, or 2b) looking at the marginal doesn’t reveal problems with conditional distributions.
It depends. If you have a simpler equivalent model maybe use that instead (e.g. models where the latent values can be integrated out analytically). If you know you model is likely to be the best one then do enough other checks or do K-fold-CV etc.