Yes, Seesaw requires a network connection to work properly. You will need an Internet connection in order to sign in and view Seesaw journals. If you do not have an Internet connection, Seesaw will alert you with a red 'offline' message bar.
Seesaw does support offline upload of journal entries, but this is more designed for a temporary loss in connection than for using Seesaw with an internet connection at all.
To add a post while offline, you will go through the add post flow as usual, but when you save the post you'll notice a red bar at the top of the screen listing pending uploads.
The next time you connect to the Internet, upload will automatically resume if you start the app, or just tap on the retry button to start uploading.