Nick here from Shopify. Good question!
The 24/7 support via live chat is available when you are on any plan. So if you are on the basic plan and have a question at 2:34 am you are free to chat with us. The best way to reach the chat is through this link here and to log in with your store details and connect to a live chat then.
Do you have any other questions about Shopify or the starting stages of setting things up? Let me know if you do.