If, prior to the regular due date of a return, an area is declared a federal disaster area and the IRS postpones filing and payment obligations, the due date for filing the return (or filing for an extension) is postponed to that date.
Any extension filed by that postponed date would be valid, however the extension would begin on the original due date and run out at the same time a "regular" extension would. For example, if the filing deadline of April 15 was extended to May 11, an extension filed on May 11 would be valid but would not run for 6 months from May 11 but rather 6 months from the original due date of April 15. If this extension was filed on May 11, the return would be considered timely if filed on or before October 15. Since the payment of taxes in this example would be due on May 11 (the postponed date due to the disaster), filing an extension would not delay that deadline.
The IRS website FAQs for Disaster Victims – Extensions of Time to File
offers information regarding filing of extensions in disaster areas. In the case of a federally declared disaster, an affected taxpayer can call 1-866-562-5227 to speak with an IRS specialist trained to handle disaster-related issues.