Yes, both the customer and the vendor can send offline chat messages to each other using Magento 2 Marketplace Buyer Seller Chat.
When a seller or a customer is unavailable for chat or offline, they can still type in the message and hit enter. Whenever the receiver is online, he/she can see that offline message in the chat window.
Please do contact us for any further queries or requirements. You can also check our Magento 2 Extensions for additional features.