Regardless of muzzle velocities, no projectile "drops" before it reaches the convergence point. You all do realize how small of a difference there is in muzzle velocities here over short distances, right?
7.7mm ~855m/s
20mm ~755m/s
R*T=D
so
Time = Distance/Rate, or Distance/855m/s and Distance/755m/s:
Let's say you fire at a target that is 350m away. The 7.7mm projectile will get there in ~.41 seconds. The 20mm projectile will get there in ~.46 seconds, for a difference of 5 hundredths of a second. What's more, that difference only matters for the first projectiles that leave the guns; .05 seconds after the first 7.7mm projectile reaches 350m, they are arriving in a combined stream.
That math just doesn't justify setting different convergences or firing the weapons independently.