Yes, after your survey has been assigned and downloaded to your device, you can conduct surveys and collect responses on your device without having Internet connection on your device.
Responses to survey questions are stored on your device until you choose to upload them. If you prefer you can switch your device into Airplane mode to save battery life while conducting surveys.
Once your device has Internet connectivity you can upload the survey responses as a batch to the Data4Action server, accordingly your survey builder account will be updated.