Indeed, it doesn't seem to be a return from the headphones nor an effect, it's more like an unintended vocal polyphony (diplophony) when he screams in falsetto. Certainly he hasn't mastered the technique.
I don't know the original track (I'm not exactly a Van Halen fan), but probably the global mix masquerades this polyphony.
If you're talking about Bananen then I'm a happy ignorant. Surely I won't miss them (except for technicalities I may be curious about), my music tastes aren't that simplistic.
Edit: I thought you could enlighten me about the possibility of a modulation effect - phaser, flanger, chorus or derivative - being used as insert or send - cascaded through a carefully crafted EQ or multiband compressor to explain the sound of the falsetto, but I guess that I'll have to accept a better explanation: not all singers have the vocal polyphony capabilities of Demetrio Stratos, but some achieve an unintended result. What a pity, I will remain ignorant about my curiosity and will have to accept Kev's hypothesis as good.