No, the Mazda brake rotor bolts on from the back with 6 bolts. The wheel doesn't even touch it.
See the 6 holes between the studs? That's the threaded holes for the brake rotor bolts coming in from the back. When you redrill them to a 5 lug, one of the holes for the 5 lug pattern interferes with one of them...no matter how you rotate it.