Feature services do not support annotation feature classes. However, if you have annotation in the map that you publish it will be in the map service. You can then draw the map from the map service in your application and edit the features through the feature service using featurelayers in selection mode. That way you get the annontation in the map and can still edit the non-annotation features.
Yes, image annotation feature services do not support annotation feature classes at present. Thus, if we want to customze and edit annotaiton features, such as annotation font style, annotation font property, font color and size, as well as other annotation parameters, including annotation edge properties in width, style, color, we can only refer to some third party annotation plugin.