It reads the page once on its way out and rewrites the tags it recognises. That is one pass over the HTML — measurable, but small, and it happens before your page cache stores the result, so a cached page costs nothing at all.
The banner's stylesheet does not hold the page up either: the page is drawn first, and the banner appears once its stylesheet has arrived, already in place, so nothing on the page moves.
It also makes most pages faster for visitors who have not agreed, because the third-party scripts do not load. Those are usually the heaviest things on the page.
Still stuck? Ask the developers who wrote it. We aim to reply within one business day.
