Hi @ywon,
The answer is: it depends. Adblockers do block many if not most 3rd party cookies, but it's because they stop the browser from making 3rd party requests. Adblockers usually rely on lists of domains, or paths that are associated with ad serving, and can also include site analytics and testing domains. Consequently, some ad-blocking lists do include Target based domains and therefore can prevent Target from loading. In this case, it doesn't matter if your Target implementation uses first or third-party cookies, because the request to Target never even happens.
Using a CNAME to route your Target requests to a first party looking domain can be an option that allows Target to run even if an adblocker is on.