Depends on the type of backup. If you're scanning or photocopying pages, you're backing up with signatures. If you're using logbook software for backup, you're not.
But you don't really need to back up the signatures. The backup is really to provide you with a reliable record to use when you follow the FAA's procedures:
From Order 8400.10 - Air Transportation Operations Inspector's Handbook
Volume 2, Chapter 1, Section 10
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21. LOST LOGBOOKS OR FLIGHT RECORDS. Aeronautical experience requirements must be shown for a person to be eligible for the issuance or to exercise the privileges of a pilot certificate. A pilot who has lost logbooks or flight time records should be reminded that any fraudulent or intentional false statements concerning aeronautical experience are a basis for suspension or revocation of any certificate or rating held. The pilot who has this problem may, at the discretion of the inspector accepting the application for a pilot certificate or rating, use a signed and notarized statement of previous flight time as the basis for starting a new flight time record. Such a statement should be substantiated by all available evidence, such as aircraft logbooks, receipts for aircraft rentals, and statements of flight operators
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and
Volume 5, Chapter 9, Section 4
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731. LOST LOGBOOKS OR FLIGHT RECORDS. Inspectors should advise airmen that they may reconstruct lost logbooks or flight records by providing a signed statement of previous flight time.
A. Proof of Experience. Airmen may use the following items to substantiate flight time and experience:
* Aircraft logbooks
* Receipts for aircraft rentals
* Operator records
* Copies of airman medical files
* Copies of FAA Form 8710-1, "Airman Certificate and/or Rating Application"
B. Obtaining File Copies. Airmen who have lost their logbooks or flight records may request copies of their files from the FAA by writing to the following:
FAA Airmen Certification Branch, AVN-460
P.O. Box 25082
Oklahoma City, OK 73125
FAA, Aeromedical Certification Branch
P.O. Box 25082
Oklahoma City, OK 73125
NOTE: Inspectors should encourage pilots to complete the flight time sections of official record forms, even though it would not be required for that specific certificate. These records document a chronological development of flight time in case personal records become lost.
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Don't know about anyone else, but I'd have no problem signing an affidavit based on my electronic logbook entries.