The $z$-value is just the test-statistic for a statistical test, so if you have trouble interpreting it your first step is to find out what the null hypothesis is. The null hypothesis for the test for CLASS0 is that its coefficient is 0. The coefficient for CLASS0 is the difference in log(odds) between CLASS0 and the reference class (CLASS3?) is zero, or equivalently, that the ratio of the odds for CLASS0 and the reference class is 1. In other words that there is no difference in the odds of success between CLASS0 and the reference class.
So does a non-significant coefficient mean you can merge categories? No. First, non-significant means that we cannot reject the hypothesis that there is no difference, but that does not mean that no such differences exist. An absence of evidence is not the same thing as evidence of absence. Second, merging categories, especially the reference category, changes the interpretation of all other coefficients. Whether or not that makes sense depends on what those different classes stand for.
Does that mean that the entire categorical variable is a "bad" (non-significant) predictor? No, for that you would need to perform a simultaneous test for all CLASS terms.
