I think you might be on to something. When I visit the page Visit http://www.google.com/accounts/DisplayUnlockCaptcha, it tells me that I should try signing in again, and when I do that, I get a popup from GSync saying that I should enter a CAPTCHA. Unfortunately, there does not appear to be a way to do that.
When I try the process again, I am back to the original Bad Authentication error message.
It is a good thing one has 30 days to get this set up.