If that is the idea, it does not work for reasons:
- further spend attempts will not be broadcasted by a node after one of the attempts is included into the mempool
- people will figure soon that miner have advantage grabbing the outputs and stop trying.
Therefore the attack, if that is the purpose, is pretty lame.
Unfortunately, this attack is still quite successful. One reason is that even miners spending the 1000 Satoshi outputs will get a lower fee (about 70 bits/kB) than with regular transactions. So the spammer spent less for the outputs than cleaning them up costs. There are currently still > 5 BTC in the 100 most spammed addresses. Cleaning them up takes about 70 MB.
The problem is that the dust limit is computed from the mintxfee and some miners have it still set to 10bits/kB. Also it take much less space and therefore fee to send to 1000 Addresses than it takes to spend from 1000 Addresses. There were several suggestion to penalize outputs over inputs when computing the required fee but AFAIK it was never done in the standard bitcoin client.