I made a test with Blakebeard The Blackhearted constructor as commander (so with +40% cannonball dmg) with a lvl9 broadside and it did 870 dmg (non crit) on each hit to normal husks in a lvl49 mission (with no modifiers). I then did the same with Swordmaster Ken ninja as commander (so +0% cannonball dmg) and the same Broadside trap in the same map, and it still only did 870 dmg non crit.
So in conclusion I would say Avast Mateys does not affect broadside cannonballs.
This is surprising as I have read multiple reddit posts where people have tested this fairly thoroughly and found a significant increase in dmg. For example this one:
However it is 2 years old, so they may have patched changes in since then.
So Im wondering now why would you ever use Blakebeard the Blackhearted as support to get +20% cannonballs, if it is only usable for the ROSIE with cannonballs which it only shoots if you are using Blakebeard as commander? (am I wrong in this?). I had hoped to get +20% dmg to broadsides by using him as support for other commanders, that would still be quite significant given the great usability of broadsides.
If you have any light to shed on this subject I welcome any help/info!