spells – Is persistent damage still damage?

Blistering Invective deals persistent damage:

Your words deal 2d6 persistent fire damage, and the target must attempt a Will save.

Energy Fusion adds a different damage type to a spell that deals energy damage:

If the next action you use is to Cast a Spell that deals acid, cold, electricity, fire, or sonic damage, select a non-cantrip spell in your spell repertoire that deals a different type of energy damage from that list, and expend an additional spell slot of the same level as this secondary spell.

Do these work together?