Is it the norm to scan Board members of businesses that are in a bank's customer base against the OFAC list? I know that OFAC requirements generally include all account beneficiaries, signers, etc, etc. But are our customers' Board members actually our customer too, at least for OFAC considerations?

The norm? No.

Some banks scan the names of an entity's beneficial owners. From memory, if an SDN owns 50% or more of an entity, the entity is considered to be an SDN as well.

It's a topic that should be covered in your OFAC policy.