But this entire thread is about a case where the captcha happens after password entry!
The point is that it is an entirely legit design, and kind of is the way you have to go when the username and password are entered together. As long as the captcha is shown regardless of the password validity, both the security properties and the amount of user annoyance due to having to solve unnecessary captchas is the same as if you had had to pass a captcha up front.
The example of Google Accounts is interesting, because they use split username and password entries. So there is indeed a natural point in the flow to show the captcha between the username and the password, which is what they do. But at least up to a year ago they were doing it after the password. So enter username + submit, enter password + submit, and if the login attempt was sufficiently dodgy get shown a captcha regardless of the validity of the password.