When someone sends you a message on your 2ndLine app number, you will receive a notification like “You have received a new Text Message” with the initial few characters of the message.

If you're not on WiFi and cellular data is off, your 2nd Line won't run and you won't get a notification when you receive a new message. Albeit, the message will be available within the app next time when you open the app and is connected to the Internet.