Well, the question, "Is philosophy useless now that we have this box?" is itself a philosophical question, and one that the people in such a world would doubtless ask; so I think the answer must therefore be "no", for this reason alone (among the other reasons detailed in the other answers). It's a bit of a proof-by-contradiction, in a way.

Even if the box had the answer to that question, it would've had to have been asked in the first place, thus also proving its usefulness.

Well, the question, "Is philosophy useless now that we have this box?" is itself a philosophical question, and one that the people in such a world would doubtless ask (I mean, you are asking, so it's obviously a conceivable question); so I think this alone is sufficient to show that the answer must be "no".

Furthermore, even if the box holds the answer to that question, it would've had to have been asked in the first place, thus also proving its usefulness.

There are many other reasons, such as the reasons detailed in the other answers, too, and they're all important; but I think this is the simplest path to a "no".