Element Damage affix on weapon has no bearing on your skills damage.
The only situation where the weapon damage affix matters is with legacy items such as the old Triumvirate or Zunimassa's boots where it says specifically "Adds +x% to elemental damage" where if you had a black damage weapon (one that just has a +damage affix with no element), it directly increases your weapon's damage to include those elements (which, since your weapon damage is increased, your skill damage is increased as well.)
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Skills are calculated weapon damage first -> skill modifier -> additional modifier (elite damage or elemental damage)
The +damage affix only affects the weapon damage calculation (or weapon dps.) After that, it is irrelevant.
In short: No, it doesn't affect locust swarm.
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Element Damage affix on weapon has no bearing on your skills damage.
The only situation where the weapon damage affix matters is with legacy items such as the old Triumvirate or Zunimassa's boots where it says specifically "Adds +x% to elemental damage" where if you had a black damage weapon (one that just has a +damage affix with no element), it directly increases your weapon's damage to include those elements (which, since your weapon damage is increased, your skill damage is increased as well.)