They wouldn't show up with a court order from Japan. They'd show up in court here with the foreign judgment, and depending on the jurisdiction, have the foreign judgment domesticated and enforced, obtaining an enforcement order from the local court. Then they would serve the bank with an order from the local court incorporating the judgment of the foreign court.
*I* understand how these things work.
I was replying to an assertion that it's easy to sue a company in a foreign jurisdiction with servers/financial assets in further foreign jurisdictions and how you could quickly and easily start an action against them, get an order, and get that order enforced in a "couple of hours".
Anyways as a party to the action now I think it's highly unlikely they'd get an order in the american court without mtgox knowing about it and then getting that order to japan/wherever, filing to enforce it and showing up at the bank/ISP/etc. and having the assets seized/frozen/etc all without mtgox seeing this coming. So mtgox would still have much more notice than "sorry your accounts have been frozen". (If they wanted they could play cat-and-mouse and move the assets once the order has been issued but before it has been enforced - the judge would be really pissed but in that case they're obviously thumbing their nose at the jurisdiction anyways.
Japan is, of course, party to the treaties which allow this, and United States law has, itself, recognized the judgments of foreign courts both in common law and under statutory law passed pursuant to the mostly Twentieth Century treaties.
Well first, depending on the government, being a party to the treaty can be meaningless. I can't speak for Japan but in some countries the government can do what it wants internationally but those treaties will not become actual domestic law until they are properly ratified in the country.
That aside, even if Japan has agreed in certain areas to have the same law as the USA that definitely does not mean an order from an American court will be enforced in Japan. Even if the Japanese court is satisfied that the American court made the correct decision in law it still might decide that America was not the correct forum or that according to their laws the proper jurisdiction was Japan. In that case you'd have wasted tens of thousands and months/years of your time to get a court order that is worthless.
I have never said that it is impossible - only that big lawsuits like this move at a glacial pace when they are dealing with domestic parties and assets - the fact that the company that is being sued here and its assets are in many foreign jurisdictions will only slow this process down further.
So like I originally said, this might not be a huge pressing concern for mtgox as it isn't likely something drastic would happen overnight.