You can not only use due.work projects for internal management but can also use for "converting your visitors into customer", due.work provides "Add to Website" functionality by which you can use any project for customer live chat...
When you integrate a project into your website as a Live Chat, you will receive all your visitors/customers messages into your project, you just have to be available to chat with visitors on your website. Each conversation creates a new thread/comment, allowing your team to manage it all from one place.
This is how it will look when you receive messages from your customers.
There are 3 ways by which you can use live chat in your website -