Those who go through the official migration paths - in the U.S.A. or elsewhere, doesn't matter - are not "illegal aliens" so that word play with "as yet undocumented immigrants" doesn't hold. People who are waiting for their paperwork to go through the official channels will have some form of proof of their application status. If they were told they could await the results while in the U.S.A they're not illegal aliens, if they were told to await permission outside of the U.S.A they are. Those who cross the border with the intent to stay without legal permission are "illegal aliens" and are in violation of whatever laws cover migration - 8 US code § 1325 in the U.S.A, artikel 197 Wetboek van Strafrecht (for those declared unwanted) and artikel 61-67 Vreemdelingenwet in the Netherlands, etc. Some of these illegal aliens violate other (criminal) laws which makes them "criminal illegal aliens" but everyone who stays in a country - any country - without legal permission has violated whatever laws cover migration into that country.