In this (somewhat special/simple) case I would expect the answer to be that you are not really confronted with 3rd party cookies. I assume by 3rd party cookie you mean a cookie that is coming from a different domain than the site you are visiting.
For example a "gmail.com" cookie when you are visiting "youtube.com".
I would be surprised if Google would not set a cookie for "google.com" when you log in to Gmail (login is via "accounts.google.com" for example).
Now if (and again, I am pretty sure that this happens) youtube is loading anything from google.com (analytics.google.com?), that will happily transfer the cookie (which in this case is not a 3rd party cookie as we have defined it before).