EM can be used to impute data, but that would be single imputation. Multiple imputation as described here would not use EM since the goal is to get samples from a distribution of possible values for the missing data.
EM imputation (or single imputation in general) fails to account for the uncertainty in imputed data. You end up with artificially inflated confidence in your results (p-values too small, confidence/credible intervals too narrow, etc.).