It's Mancur Olson's "Institutional Sclerosis" growth theory. He claimed to have shown that growth rates increase after a large shock to the existing order. His explanation for this is that institutions tend to be corrupted by special interests over time, feeding on the wealth of society. Shocks give people a chance to start afresh.
He does claim to show that the losing side in several conflicts experienced higher growth rates after wars than would be expected from historical data (the American south after the civil war, Japan after WWII, etc.). Critics point to counter-examples, but as far as I know it's considered a reasonable (though not air-tight) theory.
It depends where you're talking about. In an area reasonably prepared for disasters, they actually do bring about increased prosperity -- Florida has periodic construction booms after hurricanes, and a majority are insured, so financial losses are constrained to the big insurance companies.
On the other hand, even in a developed nation, a major disaster can end the life of an area -- New Orleans is perhaps two-thirds of its former size and looks unlikely to grow.
In this case of Haiti, a steady and dedicated stream of aid could help rebuild the country, but history has shown that the international community's attention to the desperate plight of that nation has always been short-lived.
Sadly, I fear it will be worse than before, and remain so.
There's supposedly always better situation in the future, it is pretty dubious to claim that wars and cataclysms accelerate long term development.
It depends on what you mean. Wars have historically accelerated technology development, at least in the short term.
If you mean development more generally, then no probably not. The civilian technology would eventually get developped, if more slowly without the major push of a war. In the process, people and resources are destroyed.
Life goes on, disaster or not.
There's supposedly always better situation in the future, it is pretty dubious to claim that wars and cataclysms accelerate long term development.