Is it possible to write out images from SQL Server to a mapped drive?
SQL Server can usually see a UNC path like \\server\share\subfolder

But only if the service running SQL Server has rights to that share. For example, if you're running a scheduled job, the job runs as the user for the SQL Agent Service. If you're running code directly in SSMS or a stored procedure called from your program, then the SQL Engine Service must have rights to that shared folder. 

If that user is a local user only, then it won't have rights to the shared folder. SQL Server engine and/or agent must be running as a domain user to access the volume. 

For example, we run our backups to a \\server\DBs\SQL\&lt;server name&gt; shared drive. The SQL Agent Service account has to have full rights to that shared folder for the backups to succeed. There's no mapped drive involved in these backups.