It appears something more has some of the partnership between Bungie and Blizzard. 

In a new video published by YouTuber Wayne Ng, he unlocks the 'We Ran Out of Medals' achievement by killing 20 enemies without dying. Right after, the announcer can be heard saying, "DIE, DIE, DIE", just like Reaper from Overwatch.

Also See: The People Behind Your Favorite Overwatch Characters

Check out the video below and skip to 15 seconds to hear it for yourself:

Interestingly enough, voice actor Keith Ferguson (seen in this gallery) provides the audio for both characters.