It'd be illegal since Zapdos gets Heat Wave in Gen 4 only, and a DW Zapdos is Gen 5 only. Don't think of it as "illegal", think of it as "impossible".I am well aware of Smogon's policy of dream world abilities but would it be illegal for a Zapdos to have:
The lightning rod ability with Heat Wave?
I know atm the whole Lightning rod ability is illegal with Smogon standards but would Heat wave with it be illegal if you were to allow DW abilties for a battle?