How could it? As far as I am aware, the boards have no cameras or microphones attached.
You need to attach them somehow to a computer or smartphone that has a connection to the internet and that can handle your broadcast by providing you with those things.
^^ I think you aren't understanding what broadcast means in this instance. Obviously boards don't have cameras and microphones attached - he's not talking about a television or internet video broadcast. He's talking about broadcasting moves from the board like they have been done for at least 15 years now. The DGTs will do this, and I believe the Certabo has been used for this too (Yes I'm an owner and no I don't get paid to talk about it. It seems odd how they are routinely ignored despite being the most capable on the market). I have no experience of this myself but would be interested to know what you decide on.
The Chessnut Air eboard has the option to broadcast every live match simply by sharing a link. As long as you are logged in the Chessnut app, you can create the link and share it with your friends so they can follow the game via browser.
https://www.youtube.com/watch?v=bjyHIBHTJq0&t=125s
If that works or not via Chess.com or Lichess though, I can't tell you, have not tried yet.
Best 
Hi, I run a chess club at a university. We want to buy an electronic chess board, specifically for broadcasting OTB games online. Ideally, something that can connect with either Chess.com or Lichess, allowing students to do live commentary, draw arrows on the screen, etc, with live moves appearing automatically from the OTB game. No other features matter for us, it will just be for broadcasting OTB games.
Based on my research there are only two DGT boards that support this ability:
It also seems like maybe the following gear from Millennium could work?:
My questions are...
Thank you in advance for any help provided! Much appreciated.