Will homeowners insurance cover black mold algae growing on roof causing damage?

It's not very likely this would be considered a covered loss. Maintenance issues are never a covered hazard on our home insurance policy.

Mold or algae growing on a roof would likely indicate that the roof has far too much shade or has overgrowth perhaps even in direct contact with your roof. Cutting back your overgrowth will cure the problem.

This is a normal maintenance issue and an expected incidental part of home ownership.