Do toggle abilities proc on-hit passives like Spellblade?

Do toggle abilities proc on-hit passives like Spellblade? - Like Printed on Brown Wooden Scrabble

Some champions (like Ashe) have toggleable abilities (for example her Q - Frost Shot). When I activiate such an ability, how does it proc an On-Hit passive like the Spellblade passive from the item Trinity Force? Does this behaviour apply to all champions with similar abilites, like Aatrox?

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