They shouldn't in the real world, it's just "extra info". It's the difference between "book" coding and real coding. For example, let's say a patient comes into an ortho office for a fracture, if you code the 1st dx as the fracture (correctly) and add 2-3 status place of occurrence and external cause codes, they probably aren't going to kick it out. Even if they say they don't want those codes. It is correct coding to add those. For speed, some practices will tell coders they don't want those added but from a coding and data analytics perspective it is necessary.
On the other hand, if you add place of occurrence and external cause to a commercial claim and there is any question it could be work or auto related, the commercial will probably pend the claim for more info to make sure they are the payer.
It also depends on the Z codes you are talking about.
Some practice management systems also have built in claim scrubbing edits that even if one of these is added in the system, it may drop it off before the claim is submitted. So, you would see it internally but it wouldn't go out on the claim. That is, if the edits are set up correctly and updated.