Yes, these are full versions of Office for the PC and Mac. All are available for offline use. The mobile apps (iPhone, iPad and Android phone/tablets) have many of the features of the full Office versions but are not the full version available on the PC or Mac.
NOTE: The Office 365 software is free if your account is active. Once you graduate or leave the university, your status will be changed to inactive. At that time, you will not be able to install new instances of Office 365. On devices that you have already installed Office 365, you will not be able to create/save/edit files. Instead, you will be prompted to enter a product key to re-install a previous version of Microsoft Office or purchase Office at a retail store. At that point, you may enroll via other subscription offers or purchase Office through a retail outlet.
If you experience issues or have any questions regarding this topic, please contact the Technology Assistance Center at 540-831-7500 or enter a support ticket at http://www.radford.edu/itonestop.