No. The correct/incorrect old password is just data used in a recovery process.
Google knows how you changed the password (via forgot password, via the normal change screen) and when, and how old the password is in numbers (eg you changed password 2 times after this old password).
So this data is used in a general scoring model to determite if you are a legitimate owner of the account.
So a example:
Entering the previous password, and that password was changed for a hour ago, google might allow you access with that old password immediately.
Entering a old password changed for a month ago, might direct you to the screen that allows recovery by secret question.
Entering a very old password, might get you to "get a SMS code to recover your account" procedure.
And entering a outright incorrect password might send you to the screen that require customer service interrogation Before recovering access.