Yes you can.
I understand the device is mapped as a network drive in your desktop. The way I go about this is create a bat file for the copy operation, such as:
xcopy /s Y:\*.* C:\backup\, where Y is the mapped network drive and C is the local drive you want to place your backup at. The /s modifier states that subfolders should be copied (unless empty).
Now to automatically run this script, you can use the task scheduler. Launch the windows task scheduler, create a new task ("create new task", not "create new basic task"). Go to the "action" tab, create a new action of "start a program" and point to the bat file. Go to the "trigger" tab and create a new "on a schedule" trigger, setting when you want it to run. [strike]You can set the task to "hidden", so that it will run in the background[/strike] You can set the task to run with the "System" account, so it will run in the background.
You might want to create a different task to delete your old backups, otherwise you'll be replicating the files each time.
If you want to filter what you want to backup, you may use the forfiles command. That would allow you to copy only files no older than a specific date, for instance.
If you want a more organized way and hassle-free way, you may prefer using specific backup software, such as cobian backup, AOMEI backup or EaseUS Todo Backup.