No, unfortunately Avenger's Shield uses regular +hit, not spell hit.  Spell hit is used by judgement, the first tick of consecrate, and exorcism (situational anyway).  Our righteous defense and avenger's shield both use melee hit.  Personally, I have a few +hit gems that seem to cover me most of the time. (though I do still get a missed avenger's shield on a pull once in a while, which totally sucks when the DPS starts nuking right away cos they never notice...)