The law will be overturned, the US Constitution states Congress makes laws concerning naturalization, not AZ (To establish an uniform Rule of Naturalization, Article 1 Section 8).
You are correct quoting that particular (the italics mine) line in the Constitution.
With that said, please grant my request of identifying, highlighting, copy/pasting the section/subsection in the Arizona Law (SB 1070) specifically stating where, when they will be conducting "Naturalization hearings?"
You may find these interesting. Just a few court cases where illegal aliens tried to fight the system and lost. Some involving 4th & 14th Amendment rights to State LEO’s rights in questioning legal status.
These few federal court decisions on the illegal alien issue also have direct bearing on SB 1070 signed into law:
Gonzales v. City of Peoria,
http://openjurist.org/722/f2d/468/gonzales-v-city-of-peoria 722 F.2d 468. 1983: United States Court of Appeals for the Ninth Circuit
United States v. Salinas-Calderon,
http://openjurist.org/728/f2d/1298/united-states-v-salinas-calderon 728 F2nd 1298. 1984: United States Court of Appeals, Tenth Circuit
United States v. Vasquez- Alvarez,
http://openjurist.org/176/f3d/1294/united-states-v-vasquez-alvarez 176 F.3rd 1294. 1999: United States Court of Appeals, Tenth Circuit
United States v. Santana-Garcia,
http://openjurist.org/264/f3d/1188 264 F.3rd 1188. 2001: United States Court of Appeals, Tenth Circuit
United States v. Rodriguez-Arreola,
http://openjurist.org/270/f3d/611/united-states-of-america-v-manuel-rodriguez-arreola 270 F.3rd 611. 2001: United States Court of Appeals, Eighth Circuit
United States v. Hernandez-Dominguez.
http://caselaw.lp.findlaw.com/cgi-bin/getcase.pl?court=10th&navby=case&no=993305 2005: United States Court of Appeals, Tenth Circuit
Gray v City of Valley Park.
http://www.ca8.uscourts.gov/opndir/09/06/081681P.pdf 2008: United States Court of Appeals, Eighth Circuit.
Astrid G. Estrada
http://www.ca1.uscourts.gov/pdf.opinions/09-1149P-01A.pdf February 10, 2010; United States Court of Appeals, First Circuit