If the service is published from an SDE database through ArcGIS Server/Service Manager, then updates made in the source data will sync/live update in the service.
But if it was published as a hosted web layer (copied data), changes in the original source will not automatically sync.
Another option is to add the published web layer from the Portal/Content pane into ArcGIS Pro and edit it directly. The updates will reflect live in the service, but it will not update your original local database automatically.
