Yes, it is possible to dynamically update the symbology of a published map service.
In ArcGIS Online, however, dynamic layers must be used to dynamically update symbology of a published map service. Dynamic layers can be configured after the map service is published.
Without dynamic layers, changes to symbology must be made on the layer in ArcMap before it is published as a map service.
Note: Symbology is dynamically updated to display data in real-time, and to change the appearance and behavior of each layer.