The proper term is "illegal alien," or "illegal immigrant."
An alien is a person in a country that they are not a citizen of:
Any person not a citizen or national of the United States.
Where as, an immigrant is:
"Permanent Resident Alien" - An alien admitted to the United States as a lawful permanent resident. Permanent residents are also commonly referred to as immigrants; however, the Immigration and Nationality Act (INA) broadly defines an immigrant as any alien in the United States, except one legally admitted under specific nonimmigrant categories (INA section 101(a)(15)). An illegal alien who entered the United States without inspection, for example, would be strictly defined as an immigrant under the INA but is not a permanent resident alien.
The Department of Homeland Security and Immigration and Customs Enforcement both extensively use the terms "illegal alien" and "Illegal Immigrant," especially when compared with the "undocumented immigrant" or "undocumented worker." (100-1000 fold difference)
As for what effect the AP would have, that is impossible to determine. It should be noted that this sort of thing has happened before in the general public. The term idiot used to be used medically to describe people with mental retardation. But, people would use it as an insult, sometimes by children at other children who weren't actually mentally retarded), so to prevent bullying people were encouraged to use more politically correct terms. Moron, retard, midget, dwarf, gay and other terms have met similar fates.