Should Expectation Maximization take into account the Naive Bayes' independence assumption?

Should the independence assumption on which the Naive Bayes (NB) classifier is based, be taken into account when applying Expectation Maximization(EM) to infer missing values?

The Naive Bayes classifier assumes that all attributes are independent given the class variable. Normally, the given structure of a Bayesian Network would be exploited by the EM algrithm. However, the NB classifier still performs well enough when the assumption is not met. So it is entirely plausible to have a dataset, in which the assumption does not (entirely) hold and to succesfully train a Naive Bayes classifier.

I am inclined to disregard the independence assumption as it does not (neccesarily) stem from domain-knowledge, but is just a consequence of the simplifying assumptions inherent to Naive Bayes. Am i right in doing so?