No. Your Creative Cloud desktop applications (such as Premiere Pro and After Effects) are installed directly on your computer, so you won’t need an ongoing Internet connection to use them on a daily basis.
An internet connection is required the first time you install and license your desktop apps, but you can use the apps in offline mode with a valid software license.
The desktop apps will attempt to validate your software licenses every 30 days, but for annual members, you can use the apps for up to 99 days in offline mode.
Month-to-month members can use the software for up to 30 days in offline mode.