Suppose we have a Bayesian model with data $y$ and a parameter to be estimated, $\theta$. Then the posterior is written as:
$$ p(\theta | y) \propto p(y|\theta)p(\theta) $$
Suppose that we used an MCMC to obtain draws of the posterior, $p(\theta | y)$. Suppose we then take the average of these draws and then plug the average back into the likelihood, $p(y|\theta)$, and plot it across the support on $y$. Would this distribution be approximating the posterior predictive? Or is it approximating something completely different?