Can civil pilots *ever* fly military high-altitude penetration approach procedures?
As long as you can actually make the altitude restrictions, then yes, there's no reason why you cannot request to fly the approach.  However, as a general courtesy, you should also factor in your approach speed.  ATC might not appreciate a Cessna clobbering the approach 34 miles out.  These approaches are typically flown at 250+kts, so just keep that in mind.