Yes, you can work offline on any cloud document that you have opened recently. To make one available offline, you simply have to open it.
If your cloud document shows or , open the cloud document and it becomes available to you offline. Some apps let you make a cloud document always be available to you offline.
When you're back online, your updated document is automatically uploaded to Creative Cloud and is available across all your devices.
Yes, apps such as Adobe Photoshop, Adobe Illustrator, and Illustrator on the iPad let you make your cloud documents always available offline. With this setting, you don't need to open a document before you go offline. It continues to be stored in the cloud, but your local copy syncs with any changes you might make on a different device.