Best practice on Web Chat "please wait" messaging

We are currently integrating a web chat functionality on a utilities website, where customers can query their bill, or changing plans etc. with their electricity bills. (this will be available to all customers whether they are logged in or not).

The web chat will sit top right on all paged, and when clicked, will initiate a web chat sessions. In the event of a bottleneck of chats starting, we need to design a pre-screen before the chat initiates with an agent. I cannot find any best practice information our there, so my thought was to provide the following while the user waits:

• An apology message saying that chat agents are busy.
• Current wait time: XX minutes.

Would this be considered an overshare of information to the customer? or is the visibility and transparency appreciated and considered good Ux? Any hats thrown into the ring on this one are much appreciated! A brief mockup is something I put together below as a first pass: