IMHO, I would not run the motor until I found the reason for the zero pressure at idle. The first thing I would do is examine the oil and cut the filter open, looking for particles. If nothing in the oil, it could be a broken or jammed bypass spring in the oil pump or clogged oil pump pickup tube screen.
BTW, I've heard the formula has changed for Rotella oil and may no longer have enough zinc additive to protect a flat tappet cam.