"Ad cazzum" is a sort of fake latinism, to say (in a sort of fake-courtly language) that something has been done/said/thought in a totally random way with no planning at all.
Doing something "ad cazzum" means, generally, that you've just done it without even the slightest hint of thinking before acting.
You should also add that “cazzo” is Italian for “dick” and “alla cazzo di cane” is vulgar for something done in a hurry, bumbling along as you go... (and if you close your eyes for a moment and imagine a dog happily strolling along you get the picture)
Also note that English speakers would pronounce the double-zed in "razzum" and "cazzum" as "z", whereas in Italian it's pronounced more as "ts" (i.e. "catso", not "cazo"). Additionally, the "u" in "cazzum" should be silent in an Englsh accent, but clearly spoken in Italian: "caz'm" as opposed to "cah-zoom".
(Speaking as a non-native speaker of both languages and having spent a lot more time in an English-speaking country than in Italy).
You might be underestimating how weird English orthography is.
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.
I don't know, if you tell native English speakers that "cazzo" is Italian, I assume they know it's pronounced catso. Of course if they find cazzo in the wild without context it'll be like the zz in "buzzard".
But then again, some people may think pizza is American and not make the link.
Like samatman says- knowning how to pronounce the zz in "pizza" doesn't predict one's ability to know how to pronounce it in another word.
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".
As a native english speaker this even happens to me. I read the word "awry" as "aww-ree", and was very surprised when I discovered it was pronounced "a-rye". The best bit is that I was actually already familiar with the word awry, I just hadn't connected that the word I was reading was the same word as the word I was hearing.
Same here. When young I knew the spoken and written forms of several words without realizing they were the same. Chaos and Hyperbole come to mind (think last night's debate). You find out when you use the words-as-written (cha-ose, hyper-bowl) in conversation.
You have to remember that French borrowings have a special place in English. The timeline of Middle English is roughly defined by the Norman conquest at the start, and the replacement of French as the literary standard at the end. So it's not uncommon for French words to be spelled and pronounced somewhat accurately. (Now their meaning being recognizable is obviously a completely different question...)
