Doing something "ad cazzum" means, generally, that you've just done it without even the slightest hint of thinking before acting.
(Speaking as a non-native speaker of both languages and having spent a lot more time in an English-speaking country than in Italy).
If you know some Italian, then you'll know that words are pronounced the way they're spelled. If what you know is English, there's no reason to think the zz in pizza and the zz in cazzum are pronounced the same way.
But I'm also a low-grade language nerd. It drives me nuts when I see Latin-to-English loan words with inappropriate declinations, or fancy-sounding technical/medical terms formed by combining Latin and Greek word fragments [0]. So maybe my attention to correct pronunciation is atypical.
[0] I'm not claiming that I'm actually correct in all these cases; just that I go nuts at what I perceive to be bad treatment of loan words.
But then again, some people may think pizza is American and not make the link.
You could be right. My experience is mostly from the New England area, near areas with a lot of first-third generation Italian immigrants.
* I've heard great things about pizza in Rome, but I've never been there.
How very dare you. With only 56 rules applied in order, you can easily predict the pronunciation of a word from its spelling 85% of the time.
I'm still taken by surprise by how English words I've read often but haven't heard spoken are actually spoken by native English speakers. My classic example is the word "nonchalant", which I always assumed would be pronounced in what is to me an English accent, as "non-CHAH-lahnt" but is actually pronounced in a French accent as "non-chah-LAWn".
I probably still do this.
I bet a whole lot of Americans are the same way. They just pronounce it correctly out of inertia, and not some elementary understanding of Italian.