If I purchase the avatar upgrade, "Dark Strength," can I add a gold power die to Captain Bones' attacks (in the final battle) when he is playing the organ? In other words, do my canon attacks benefit from the upgrade or does the upgrade only apply for Bones' regular attacks?

Difficult call.

When attacking with a cannon the monsters don´t use their regular dice and monster abilities do not apply (as per the FAQ).

"Dark Strength" says "roll an extra gold die when attacking" so by RAW it seems to apply to cannon attacks as well.

The question is also valid for a Doom card (which can be in play in the island level with the shipwreck) or similar upgrades.

I can´t say anything how this applies to Cpt. Bones playing the organ, since I don´t have access to the text to evaluate at the moment.