For concreteness, suppose they have 100,000 BTC previously spread out over that many addresses, and start sending out 10-satoshi transactions between those addresses with 1 satoshi of fee. They can send 10^13 (10 trillion) such transactions before they run out of coins. Would the network handle that?
Not exact numbers, but useful numbers for reasoning, approximately correct: You can pack about 20,000 xns into a block. To outcompete other xns you need to pay > 0.0001 btc per xn. Filling a block to deny service for 10 minutes requires 2BTC. 100,000 BTC would deny service for 500,000 minutes, about 11 months.
In practice I would expect fees to rise quickly, as miners observed the attack and began to take steps. I could see such an attack lasting for a week or two, depending on how quickly measures were taken and how well co-ordinated the major mining pools were. There are a zillion ways to break the attack vector. Miners are ever and always the defenders of the network.
Interesting calculations. You forgot to take into consideration that larger sums get more priority so you most probably would only disrupt a portion of transactions
