Can symbology be updated from a referenced WMS service?

No, it is not possible. This is expected behavior based on how Web Map Services (WMS) function. Once a WMS service is published, it becomes static and is used for visualization purposes; direct edits cannot be made to it. Any changes made to the layer outside of the web map do not directly impact the layer in the web map. To update the style of a WMS service referenced in ArcGIS Online, it is necessary to update the source service. This action cannot be done from ArcGIS Online; it would require the same client where the WMS service was originally published and a similar workflow to republish it.