Can I hide chats I don't want to see in my queue?

Yes!

This feature is for Organization Representatives (Recruiters). You may use the visibility icon in the chat to "hide" this chat. It doesn't completely hide it, but it will pin the chat to the bottom of your chat queue so it does not interfere with your most recent chats. This is also reversible in case you would like to "unhide" the chat and allow it to bring the chat back to the top when responses are received.