I'm very formal that when you use "Add > Add layer from Web > A CSV file", no data is stored in ArcGIS Online.
However when you drag and drop the CSV in the web map or do "Add > Add layer from File" then the data will be stored in ArcGIS Online.
I just tried to be sure and noticed that the workflow with "Add > Add layer from Web > A CSV file" is broken.
This is a major regression that we are going to fix ASAP. I will post an update here once resolved.
Note that there is a workaround to that issue, while the application display "Loading data" (before it says Loading failed), if you resize the browser window, the application will load just fine.