Is it possible to add a csv file with addresses to be placed on the map using the add data widget available in Web AppBuilder?
Yes. Please see the help topic,
Add Data widget—Web AppBuilder for ArcGIS | ArcGIS
Hope this helps,
Any chance I can upload the csv I'm trying to use? I thought I was following the help topic but I must be missing something obvious.
> ... I thought I was following the help topic but I must be missing something
What issue are you having? Can you post a screenshot or the error message? At which step in the help doc are you getting stuck?