Even if they find the black box, which might be tricky with the beacon batteries only lasting a month, there's still 2 problems.

One is that it only holds 2 hours of data. If the last 2 hours were just gliding into the sea, that's useless.

Second - if the plane was deliberately sabotaged by the pilots, they could have pulled the circuit breaker for the black box which again would render it useless.