In the personal income and consumption report noted in the previous post, the BEA provides a link to a description of how hurricanes and other disasters affect the economy. At first blush, it may not seem very exciting, as the bottom line is they basically punt:
BEA is not able to estimate the effects of a disaster on GDP because the effects may occur with a lag, and they cannot be disentangled from the regular source data that BEA uses to prepare its estimates.
But there commentary provides a pretty nice tutorial on the basics of national income accounting.
GDP is a measure of the Nation’s current production of goods and services; as such, it is not directly affected by the loss of property (structures and equipment) produced in previous periods. GDP may be affected indirectly by the actions that consumers, businesses, and governments take in response to disruptions in production or to the loss of property, but these responses are not amenable to precise quantification; moreover, the responses may be spread out over a long period of time.
There are also some details on how insurance payments and services are treated, just in case you can't sleep without knowing.