One more for Jack's method. I use a cheap machinist center punch knock-off, but the principal is the same. Create a small depression so the drill bit doesn't wander, and create geometry needed for the two cutting edges of the bit to bite into.
That said, you should be able to get away without it in a pinch. Drill bits need to be at least decent quality, and I suppose annealing the PE might not hurt, though I've never done it myself.