glamph
All of our live chat is staffed with real people, yes. If it was telling you the wait was only 4 minutes however, 20 minutes does seem a bit unusual. I'd check to be sure your browser does not have any ad or pop-up blockers enabled, as those can sometimes keep the chat window from appearing normally.
It also may be worth using a different browser entirely and/or using an incognito mode window to try again. Another option would be selecting Continue without logging in if you create the case in incognito mode without signing into the account.