No. Refer to the ruling on Domino – Not Really a Party Girl (see link below) that sets the precedent an Energize ability would not trigger from the Used Pile. Therefore, Harley Quinn’s ability would not trigger the Energize ability from another rolled Character die.
In a broader perspective, in applying Energize for any ability that has a ‘roll and check result’ effect you must first check the Play Area in which the die is rerolled. If the Play Area is a place for unrolled dice (e.g. the Used Pile and Prep Area), then abilities that can trigger due to the rerolled result of a die (e.g. Energize) would not occur.
If the Play Area is a place for rolled dice (e.g. the Reserve Pool and the Field Zone), then such abilities can occur.
Recap of the Domino ruling:
Domino’s die was in the Field Zone and an ability forced the reroll of that die. Per this ability, dice rerolled on an Energy face are moved to the Used Pile. If Domino rerolls a double Energy face, the die is in a rolled Play Area (the Field Zone), hence her Energize ability would trigger. The forced reroll ability must be completely resolved before you can proceed to the Energize ability. This moves Domino’s die to the Used Pile. When her Energize ability (deal 1 damage to an opponent and reroll) is initiated, the die is now in an unrolled Play Area (the Used Pile). Therefore, if she rerolled another double energy face, her Energize ability would not trigger.
In comparison, if the forced reroll ability did not have the “move to the Used Pile” stipulation, the Domino die in this case would have moved to the Reserve Pool, and in this Play Area her Energize ability could be triggered again.
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