Yes, the EQ on my iPhone 4 does work with the HP-P1. I don't believe it overrides anything, just changes the signal out.
I'm actually happy it does as I find the non-eq sound to be very light on bass. The Electronic setting suits my tastes the best.
I started using EQ apps to bring the bass out a little but found players like ONKYO sound so much better than iTunes that additional EQ was not needed. I leave the EQ off.