They can but I think they request formally not to say the oath. There might be something on the CD on this under "oath."
http://www.drbilllong.com/FreeExercise/Girouard.html
Naturalization Oath of Allegiance to the United States of America
Required for legal immigrants to become citizens of the United States
Oath: "I hereby declare, on oath, that I absolutely and entirely renounce and abjure all allegiance and fidelity to any foreign prince, potentate, state or sovereignty, of whom or which I have heretofore been a subject or citizen;
that I will support and defend the Constitution and laws of the United States of America against all enemies, foreign and domestic;
that I will bear true faith and allegiance to the same; that I will bear arms on behalf of the United States when required by the law;
that I will perform noncombatant service in the armed forces of the United States when required by the law;
that I will perform work of national importance under civilian direction when required by the law;
and that I take this obligation freely without any mental reservation or purpose of evasion;so help me God."
United States Immigration and Naturalization Service
http://www.immihelp.com/citizenship/naturalization-oath-ceremony.html
Notice section on changes to the oath