Presumably you mean whether or not it ricochets (startoss comet/shower) and not whether you get the damage bonus(startoss style).
Throw Athame (from the Magus archetype Spellblade is its own standard action (and not the attack action, so no vital strike either).
Startoss Comet/Shower is also its own standard action (and not the attack action, though it has special rules for vital strike).
TLDR: They don't.
However, it 'acts as a dagger', so you should get the static damage bonus just fine from the style in general.
