Hi Amber,
You can "add" custom widgets to use in Web AppBuilder for ArcGIS Developer Edition, which is hosted on your own machine. When you run Developer Edition, you would sign into and connect to your ArcGIS Online organization to leverage its web maps and data resources.
Custom widgets are only stored on your own machine, they are not added to ArcGIS Online.
Portal for ArcGIS (which is part of ArcGIS Enterprise) enables you to reference custom widgets as items. FYI, Portal help topic, Add custom widgets—Portal for ArcGIS | ArcGIS Enterprise
Hope this helps,