Continuity mistake: When Holloway is hanging outside the Cube from the rope of clothes, it would seem that it disappears at the moment she falls. We see her climbing up toward Quentin, and the rope is around her waist. Then they're holding hands face-to-face, and in the next shot when she slips, the rope stays still. Then, as Quentin goes back inside, it's disappeared entirely, and he doesn't take it back in with him. (00:47:00)
Continuity mistake: Throughout the movie, Leaven's glasses have a crack in them that appears and disappears.
Answer: It's established that sound travels throughout the structure reasonably well. Also, they didn't travel relatively far, even with the rooms shifting.
Actually, considering the distance that they travelled and the injuries he sustained, Quentin would have had extreme difficulty catching up. It looks like the 3 travelled upwards at least 12 cubes, meaning Quentin would have had to climb up each one with the chance that any of the rooms could be trapped fast enough to catch up to them with enough strength left over to kill Leaven.
Adrenaline is an extremely driving force, so I'd still consider it entirely possible it happened that way.