I don't think they have a recovery tool in place, so you would probably lose your bitcoins forever if the server went down. But in theory, whenever a user sends or receives money, they are supposed to get a set of signed transactions that they can broadcast in order to exit unilaterally with their new balance, without needing further assistance from the server. If the users keep a local cache of these signed transactions (which I do not think is currently being done, but it might be), then the user can broadcast them even if the server disappears, and thus get their balance out.
There is an important caveat, though: when you receive money in this implementation of Ark, the default way that happens is through something called an "out of round payment." In that mode, you *do* get signed transactions that you can broadcast at any time, but they do *not* offer a true unilateral exit. (But it's not as bad as it sounds, keep reading.) The transactions are timelocked, and some of their inputs can be doublespent by the server if he colludes with other users. If he did that, your exit transactions would be invalidated, and you would lose money.
But that is only the "default" way you receive money in this implementation of Ark. There is a second way to receive money, called an "in round payment," and if you receive money *that* way, the server does not have the ability to doublespend the inputs to your exit transactions, so you have a "true" unilateral exit.
Also, I believe this Ark wallet does something called a periodic refresh, and whenever it does this, your coins should automatically change from "out of round" to "in round," thus (eventually) giving you true unilateral exit even for coins received the "default" way. I'm not sure when these periodic refreshes happen. As a further caveat, if you "miss" one of these periodic refreshes (e.g. your wallet was offline), and you don't come online within a grace period after that, I believe your exit transactions become invalid anyway, and the service becomes fully custodial.