If this something you care about - test it.
Tom Leek's answer is dead on in that how the cookie, account and password connection are totally dependent on the nature of design. It's actually an incredibly bad security practice to put a password or a permutation of the password in the cookie - so there is always some server-side logical connection between the cookie and the account.
Ideally the security requirements are documented and the design is well thought out to balance risk with expense, processing requirements, and user interface desires. But that's not always ideal - session and cookie management often falls through the cracks between developers, designers, and security engineers.
It's also a part of the code that generally isn't published as public knowledge.
I can tell you from experience in using google accounts, that a password change on one system has generally provoked the need to reenter the new password on other systems hours later. Couldn't tell you if it was timeout or related to how the sessions are managed. Also, I have no reason to believe that what works one way today won't change tomorrow.