I doubt they can do much about it if it's hosted in Denmark, Slovakia or some Eastern European country. The only reason the Silkroad was shut down was because it was located in the United States which made it incredibly easy for the authorities to get hold of them. The same thing happened with Napster.
Actually the biggest downside I can see to the DGS is that it might place downward pressure on NXT's price. There's a lot of NXT whales, who can't pull their wallets without crashing the value of NXT, and yet are paper millionaires who want goods & services.
Much like I feel the Silkroad, although it brought some publicity to Bitcoin, may had been the reason why Bitcoin had no value for a long time. If you have whales fireselling BTC to acquire drugs and guns then it lessens the value. We are seeing a similar trend where mass merchant adoption of BTC only seems to be bringing down prices (due to merchants, seconds after getting their BTC, are fireselling for $Fiat as they have business expenses and employees to pay and most businesses take less than 10% in revenue as net profit. Merchants are dumping 90%+ of the BTC they are receiving).
##
There will be a downwards pressure on NXT through buyers, but the media attention might be able to offset it. We will see what the net-effect will be.