This is incorrect. Traffic is not ‘routed through a pihole’, it is a DNS resolver which returns a localhost address for blacklisted domains. Basically it causes your browser to try to load blacklisted content from a webserver running on your local PC, which (for the average user) doesn’t exist and so it gives up.

More and more websites do detect this and it can be as simple as checking for the presence of a variable that should be set if some piece of JavaScript from an external domain was loaded. In such a case it wouldn’t matter if you refused the tracking code due to PiHole or an adblocker extension. Actually the adblocker would even have an advantage here, as it would be capable of manipulating any client-side scripts that trigger these warnings, whereas Pihole has no interaction with your browser at all.