Sorry that this is not really a SAS question but i know many of you will be able to help me especially if this is too easy. Is it always the case that if we don't account for the clustering that we may underestimate the standard error? Under what circumstances and why that standard errors will be either overestimated and underestimated?
Cluster, as in a clustered sample survey? Or, cluster, as in a feature of the data? Though I'm not sure that it matters.
One can easily construct a data set in which the SE for the naive estimator (e.g. un-clustered) is greater than that for the adjusted estimator.
In general, model based adjustment reduces the error term. That's one of the main reasons for modeling. Occasionally, it can increase the error term; that may be because a (some) predictor(s) are not related to the outcome. It can also happen if the model has the wrong functional form.
An exhaustive answer to your question is the subject for a book.
If you ignore positive correlation within clusters you will underestimate the standard errors of time-independent predictors and overestimate the standard errors of time-dependent predictors. The opposite is true for negative correlation.