Not exactly. While it is possible to become a Guardian 'supporter', and contribute financially in exchange for ad-free browsing after you identify yourself by logging in, you are not free from tracking by third-party ad companies as you browse their site.
The parent comment you are responding to said "I think the business model would generally incentivize much more user-friendly operational decisions than an ad-sponsored approach does." and while this gives you a superficially cleaner browsing experience, ad companies continue to track you as you browse the Guardian's website, harvesting data which can be used to manipulate you elsewhere on the web.
The Guardian could choose to disable all third-party trackers for logged-in paying supporters, but they do not. For privacy conscious readers, the only way to achieve what you want is to install an ad-blocker and a browser extension such as Privacy Badger. Contributing to the paper provides little or no privacy benefit, though it's always a good idea to support quality journalism, so if you do it, do it for that reason alone.