Is it possible to transfer an open conversation between an agent and a customer in LiveChat to WhatsApp?

Yes, that can work. There are two options on how to make this possible:

a) It is the easiest if the agent sends the wa.me/ link to the customer in LiveChat and then assigns the new conversation to himself.

Or

b) As soon as the customer has submitted his phone number, the agent can open a new conversation via WhatsApp.