The issue isn't whether the user can navigate to the folder. The issue is whether the service account for SQL Server can work with the folder.
Trying to do a simple backup to that folder seems like quite a good test. You should be able to trap failures on that pretty easily.
Another left-field approach might be to put these into an Agent job, where you use Powershell job steps to make sure the folder exists, has permissions for the SQL Server service account, etc. And do that before the T-SQL steps that move the metadata, etc. The job could read details of the databases to modify from a table in some DB. Clearly you could do that with xp_cmdshell commands from the DB but we try to avoid enabling that.