I believe in AZ, as an enforcement policy, state and local police officers are told not to check or ask for the legal status of people. This was left to the feds. This law was passed because the feds failed to control the problem.
The way I read it this law does not give the local law enforcement any new powers, just re-enforces current ones and most importantly gives protection to the local individual law officer from civil law suits.
“some guy is reading the newspaper on a park bench” does not arouse reasonable suspicion now does it so it would not be lawful to check his legal status, unless of course he was doing coke off the paper.