Can civil pilots *ever* fly military high-altitude penetration approach procedures? Let's say I'm flying some business types in a Gulfstream III (an approach category C aircraft) from Stockton to Palmdale to meet up with some USAF types there (new airplane deal, wooo!).  Can I accept/fly the HI-ILS approach to RWY 25 at KPMD:



or am I only allowed to accept a STAR or vectors to a standard ILS approach to KPMD?
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.