As it is right now, when a ArcGIS Server hosted WMS layer is being loaded into ArcGIS Online / Portal for ArcGIS / Esri Javascript API, it actually loads the corresponding MapService instead. (found out with network monitor) Therefor, RefreshInterval settings works on those layers.
When I load, for instance, a GeoServer-hosted WMS Layer, ArcGIS Online lets me set the refreshInterval through the menu as normal, but does nothing with it.
Same goes for setting it on a WMSLayer in the Javascript API.
This confuses me, as it's a client side timer & reload so it should be relatively easy.