It doesn't matter if you accept cookies or not. If the site you visits presents content ( script, button, whatever ) served from another site, you may be tracked server side via log + all the goodies in your request header.

With No third party cookies enabled, the only thing the hosts of the other content should get is IP address. It's possible that they are storing that and cross-referencing against the ip logs otherwise but that would lead to a lot more embarrassing situations considering how much more likely it is that 2 different people are behind the same NAT than logged in to the same account, and it would be explicitly going out of their way to track people who clearly were trying to opt out.