No, as I explain in my answer to the question Medix2 linked in comments, applying the same (seemingly accurate) ruling suggests that the combination does not work.
Specifically, persistent damage is "dealt by" a Condition, not the character that inflicted the Condition. By extension, the spell is not "dealing" damage in the sense that Energy Fusion implies; it would be different if blistering invective had a duration over which it did damage instead of being the Condition persistent damage.
But... this is something a GM could easily rule the other way on. It will increase the effectiveness of Energy Fusion a bit (I believe the "expected" duration on persistent damage is approximately three ticks) at the 'cost' of using less up-front damage. A 4th level blistering invective does 4d6 damage to 3 creatures whereas a 4th level fireball (ye olde go-to for spell damage comparison) does 8d6 to everything in a 20ft radius. It takes a second round for BI to catch up in damage assuming fireball only hit 3 targets.
However, GM's should take care as there are other spells that trigger persistent damage, and it's possible that, depending on group composition and enemy types/density/etc., adding sometimes 2-4+ times the bonus damage from Energy Fusion (in addition to the non-damage effects of such spells) could cause issues with spells hitting well above their weight.