Of course they would. And what's the problem? None
First they are found, and even if thousand miles away, they contain all data, even the position of crash.
The problem is more along the lines of accidental ejection, especially if such an accidental ejection could itself cause safety issues (damage to the aircraft, etc.)
Airbus vs. Boeing have been debating this for months. From an NTSB meeting last year:
Boeing, Airbus at odds over black boxes that eject