Smite

Yes, if the unit's controller applies the protective death replacement before Smite's replacement; if they apply Smite's first, the unit is banished. All of these effects replace the same death event, so the affected unit's controller chooses their order.³⁷²

Smite's "if it would die this turn, banish it instead" is a replacement effect.^369.1 Guardian Angel, Zhonya's Hourglass, and Tactical Retreat also replace a unit's death. If the controller applies one of those protective effects first, the kill action does not occur and the unit is healed, exhausted, and recalled.^370.1.a.1 For the first two effects, the gear also dies in the unit's place. None of those replacement actions is another death event for the affected unit, so Smite has no qualifying event left to replace.^370.1.b

If Smite's effect is applied first, it replaces the unit's death with banishment. Banishment is not a kill,^428.2.a so none of the protective effects applies afterward.