Persistent Damage is Dealt
Damage "recurring" seems appropriate to what is written about damage being dealt from a damage roll:
In the midst of combat, you attempt checks to determine if you can damage your foe with weapons, spells, or alchemical concoctions. On a successful check, you hit and deal damage. Damage decreases a creature’s Hit Points on a 1-to-1 basis (so a creature that takes 6 damage loses 6 Hit Points).
Damage is sometimes given as a fixed amount, but more often than not you’ll make a damage roll to determine how much damage you deal.
With persistent damage coming from a spell, it would also qualify as damage dealt by that spell.
Persistent Damage is Damage
The wording of persistent damage has been updated as of the 3rd Core Rulebook FAQ/printing to be more clearly both a condition and damage.
Persistent damage is a condition that causes damage to recur beyond the original effect. Like normal damage, it can be doubled or halved based on the results of an attack roll or saving throw. Unlike with normal damage, when you are subject to persistent damage, you don't take it right away. Instead, you take the specified damage at the end of your turns, after which you attempt a DC 15 flat check to see if you recover from the persistent damage.
A bonus to damage applies when that damage is rolled, and this wouldn't be any different.
It's worth noting that enervation does not have a basic Fortitude save, so the damage with Dangerous Sorcery wouldn't be changed by the degree of success:
- Successful Save: 2d8+4 persistent negative damage
- Failed Save: 4d8+4 persistent negative damage
- Critically Failed Save: 4d8+4 persistent negative damage