If Smite the Deathless doesn't deal damage to the target creature (perhaps because that damage was prevented), the additional effects will still apply. It will still lose indestructible, and it will be exiled instead of dying that turn.

You can target a creature that doesn't have indestructible with Smite the Deathless. It will still be exiled if it would die this turn.

The damaged creature will be exiled if it would die for any reason that turn, not just if it dies due to damage from Smite the Deathless.