Yes, although not all of the activities are optimized for offline use quite yet.
Your MOOD and HEALTH ratings will be recorded and uploaded to the server the next time your are connected to the internet. The activities in RELAX will also work correctly if you have the meditation files downloaded, as should GOALS.
THOUGHTS will work but your entries won’t be stored for later use.. You may use it to analyze your thoughts at any given time however.
Your Progress, Community, Hope Board, and Guided Paths are only available when you are connected to the internet unfortunately.