In the case of survey weighted data, one can revise weights to handle missing data, but that requires that you have weights which apply to homogeneous data sets, such that within each such subpopulation or stratum, you have "ignorable nonresponse." That means that the mean of that group could be substituted for any missing case, if you were to handle this as imputation.
My experience was primarily with continuous data, where auxiliary (regressor) data was available for the population. The use of regression for imputation, however the data were selected, is useful regarding nonresponse, even if nonignorable. "Nonignorable nonresponse" means that you cannot use the mean of a group, because the mechanism behind the nonresponse may be unknown. If you use regression, and apply it within fairly homogeneous groups where the model used does apply, then you can reduce this problem, though there may still remain some unknown factors.
One great advantage of regression for imputation is that you may easily estimate the contribution that missingness has to variance. Even when you can substitute a mean, unless you do something further, you will automatically understate variance, but regression imputation, via the estimated variance of the prediction error, has a solution imbedded. Further, because the estimate of sigma is impacted by bias, the estimated variance of the prediction error may be a good measure of overall accuracy. You may also estimate the variance of the prediction error for the predicted total. But note that this is not just the sum of the estimated variances of the prediction errors for the individual missing data cases.
For any kind of missing data imputation, or reweighting, it may be very advantageous to break the population into homogeneous groups. For many cases, you might want to research the term "response propensity" groups.