Can I claim the non-recoverable depreciation loss portion on my taxes after Hurricane Harvey?
No, this answer has nothing to do with non-recoverable depreciation loss. Non-recoverable depreciation loss on property from a hurricane is the portion of loss that the insurance company will not pay you for even if all repairs are done according to the detailed Loss Claim Summary. It is considered a LOSS of value due to the hurricane event.
Can I claim the non-recoverable depreciation loss portion on my taxes after Hurricane Harvey?
According to the IRS Publication 547, under "Casualty", losses are deductible during the taxable year that the loss occurred. You will find that page 14 and 15 is most helpful as it has information directly referring to Hurricane Harvey.