I would be careful with the use of "move out". By definition, vacation and traveling for a short time does not change the permanent address, and from this point of view, it is OK to mail the application from Tijuana Mexico or Nassau or any vacation place to the Service Center. (One should remember to be back from vacation for fingerprints and the remainder of the Naturalization process.)
Moving out (i.e. moving the permanent address to overseas) is another story as it rightfully may lead to believe that the applicant has relinquished permanent residence in the United States.
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Detroit DO - NSC
09/28/98 Entered on K-1 (Fiance) Visa
12/19/98 Married with US Citizen (still happily married 9 years after )
12/24/98 Filed I-485, I-130, I-765 in OKC (NSC)
01/03/99 Moved to Texas (TSC)
05/xx/00 Moved to Eastern PA (VSC)
11/xx/00 Moved to Central NJ (VSC)
03/19/01 LPR
03/xx/03 Received GC dated 03/19/2001
03/20/07 N-400 Priority Date
04/12/07 FP done
09/19/07 Interview passed
10/26/07 Naturalized Citizen