am i able to access my iPad files even when my device is shut down?
will the answer be the same if the iPad's battery is completely depleted?
For the iTunes Backups section, yes, since it is just showing the files in an iTunes backup. Just click on the button to Browse Backups on the screen asking to connect a device.
All other folders of iBrowse such as Media, Apps, and Root (with Jailbreak) are a direct connection to your device and read the data directly from it without requiring an iTunes Backup, so your iPad needs to be connected for those.