I don't believe Bittrex is licensed as an MSB (which also requires being registered/licensed in each state within the USA where you operate). Some people assume that since they do not have fiat deposit/withdrawals, that they are not considered an MSB and don't need to be licensed. Time will tell if that assumption will hold....
They can do whatever they want. On Black Friday, they seized Pokerstars and Full Tilt Poker (domains and bank accounts) and forced compliance. In that situation, users were lucky that Pokerstars immediately swooped in to repay everyone, pay all fines levied by the US government and quickly prohibit US customers. Everyone was repaid.
Given the way the indictment against BTC-e was written, it may as well have been a darknet site. They called both the exchange and its customers criminals, and associated the exchange almost purely with black hat, darknet and general money laundering activity. As such, I don't have much faith that they are interested in paying out anyone (if they were able to seize anything at all).
No idea if anything significant was seized. Banks in Mongolia... Okpay in Czech Republic... BTC and ETH wallets were moved today but no idea who moved them (BTC-e or government). But the feds love to claim ownership of "criminal" funds and it sure is strange that they didn't mention anything in the press release.