I vote that serial number information would hands-down not be considered a "publicly available piece of information" in court.
Serial numbers are generally used to corroborate ownership of an item in legal scenarios (and may count as a conditional representation of PII).
Apple uses them as unique identifiers to authenticate their devices and tell them apart, and very presumably protect against various forms of fraud.
Where SecureROM is up there in terms of being buried pretty deeply in the SoC, I imagine the serial number is on a similar level in terms of not being modifiable/forgeable. So the "device serial number" relationship is pretty indelible, you can't change it. And given that the way the relationship works is that you buy the hardware and then it becomes your property, you also effectively "own" that serial number to a relatively concrete extent. Thus, I can see slapping a theft charge on someone who runs off with the serial number of a device they did not own.
There's probably a much more concise way to wrap up the "nope" - the above points are somewhat general - but TL;DR, I really don't think that would work.