Hi coreydep,
Adobe Creative cloud desktop app helps you activate your apps and also in keeping them up to date, you can definitely choose to turn off sync and nothing will be synced to Cloud.
However, the applications connect to server once in 30 days to make sure you have your products activated and up and running in order to do that it needs internet connection.
Cloud features are optional it is not necessary to use the cloud space as that is given to you as a part of your subscription but you can choose not to use them.
See how you can turn OFF sync feature in Creative cloud app: Synchronize settings using Creative Cloud
Also see the below links to know more about Adobe Creative Cloud sync feature:
Browse, sync, and manage Adobe Creative Cloud assets
Sync application settings with Creative Cloud
Use the Adobe Creative Cloud desktop app to manage your apps and services, download apps, share files, find fonts, and m…
Adobe Creative Cloud desktop app: Questions and answers
Let us know if this helps.