(This is why some browsers have a setting like "third party cookies after visited in a first party context" - first party for login, third party for logout. But advertisers screwed this up by asking sites to do full frame redirects through them. )
No it isn't.
OAuth2 doesn't specify cookies in the entire spec and definitely doesn't require third party cookies, especially for logout.
Here's the RFC: https://tools.ietf.org/html/rfc6749
Spec: http://openid.net/specs/openid-connect-frontchannel-1_0.htm
Edit: I should say, this spec also doesn't require cookies - you can use HTML5 local storage or another mechanism. In practice however, if you log into a Google service like YouTube, or a Microsoft service like Outlook, or a Facebook third party like Spotify, they use cookies.
Maybe you are thinking about displaying the logged in state for things like Like Buttons or other social widgets that you'd be signed into such as Disqus or Facebook comments?