Does a Hammerdin profit from the elemental damage of Tiamats shield?
No.
All the "Adds X to Elemental Damage" work only for melee attacks.
Blessed Hammer is a spell, and spells generally benefit from "+ % Elemental Damage" or "- % To Enemy Elemental Resistance", but Blessed Hammer is pretty unique and it deals not elemental, but Magic damage. AFAIK, there are no items with bonuses to it. So the only way to boost it is from "+ X to Skills" bonuses and from Paladin's Concentration aura.