i'd like to have access to it from my favorites in a way that's browseable.
Tim - I don't believe there's a way to add a FTP site as a folder connection in ArcGIS Pro. There is an ArcGIS Idea about FTP Direct Connections in ArcGIS Pro. It's listed as Open for it's status. I'd recommend voting for this idea so it's gets more visibility to the ArcGIS Pro community and the developers.
Hope this helps!