Yes. Let’s say you try to implement a 2-component mixture model by taking a continuous variable \lambda \in (0, 1) to be the mixing proportion and then you take a bunch of uniform variables \beta_n \in (0, 1). If I evaluate \textrm{normal}(y_n \mid \mu_1, \sigma_1) if \beta_n < \lambda and evaluate \textrm{normal}(y_n \mid \mu_2, \sigma_2) otherwise, then the information about the selection doesn’t make it back to \lambda.