Yes. Files you access using the Oracle WebCenter application on your phone or tablet are the same files you access when you are in the office. As such, they are protected with enterprise-level security chosen and controlled by your company.
The Oracle WebCenter Content app uses enterprise-level authentication to access the content server, and you can set a passcode on the setting page to lock the app after a specified time to keep others from accessing your files. Any files downloaded to your device are encrypted and you cannot access them outside of the Oracle WebCenter Content app.