A good question! If you open the Debug Log (scroll the the bottom of the Settings tab) and search for DocumentPickerSyncService you should see the path mentioned to provide a clue. It will depend on the provider for the folder as to whether all the information you need is contained there.
As to how a removable device will be handled, the honest answer is I'm not sure. I haven't specifically tested for that possibility. Looking at the beorg code, the error handling will catch that the request to start accessing the resource (i.e the folder) has failed and return 0 files and directories to beorg's sync process. However that may cause beorg to think those files have been deleted and remove them from beorgs internal cache. I'll need to look into this. I'm assuming your use case here is a work laptop which doesn't allow sync apps to be installed?
My work case is complete home data (like bank passwords and such) that I want to ensure don't fall into the wrong hands. Dropbox and Git can do this job as long as I encrypt key things, but, even then, they are not perfect. Syncing thru a USB key to private areas on my devices seems much more secure. If you get this to work, it's a solid sales point for BeOrg for people who want to grow their Org files to cover all aspects of their life and need security. Also, you can get a MFI-certified 1TB USB key for <$40 which will pay for itself over an $8/mo NFS in short order. I might even consider looking into encrypted keys.
PS: perhaps BeOrg should first check(?) if the parent directory for the stuff to sync is there. If it isn't, then assume it's been removed and handle appropriately. If it is there, sync as usual.
What do you think?
Update: I'm not seeing DocumentPickerSyncService in the log (possibly because I'm using Working Copy and Github?!?). I also looked for variations (like "Picker" and "SyncService"). What I found mentioned filenames, but not folder names.
Here is an example of what I'm seeing in the debug log (this is on the Simulator however)
I'll have to look into in more detail how beorg handles folders on external devices. I will see what I've got to facilitate doing this (I currently only have lightening cable devices, maybe lets see what is announced later today!)
I went through the Log again after restarting BeOrg. BeOrg seems to be set to "Choose Folder" sync method. The Log does not have any DocumentPickerSyncService entry. I was previously seeing ORGSyncService log entries, but I'm not seeing that in this log. Basically, reading the log backwards, I'm seeing:
If there is nothing to sync you won't see that particular message. Make a change to a file in beorg and then hopefully on sync you should see that message.
(beorg should be in control of the sync with your setup.)