Well, the worst they can say is no.
I've just never heard of any non-pilot getting experience counted towards ratings/flight time. I'd sure as hell put it on a resume, but whether or not the FAA will let it go towards total time is something else.
And believe me, I see both sides of the argument, to an extent.
I would argue that quite a few of the 1,500 hours a typical applicant utilizes toward their ATP are of one of two varieties, monitoring a student while acting as a CFI or monitoring an autopilot in some sort of cargo hauling op. Functions that, if loosely defined, I could argue that I perform as well in my military flight engineer duties.
From the CFI standpoint... I, as a qualified FE, routinely mentor and train junior pilots on the aircraft systems and performance. I also back them up during their pilot training, giving insights to how the aircraft handles in different situations and giving input in how they might be able to over come some of their problems with the jet. You would be AMAZED at how much input I can give from a bird's eye view of the situation that the instructor pilot may not be able to see to correct.
From the autopilot monitor... I would love to be able to tell you how many times I have had to give a direction to a pilot to correct a situation that could have led directly to my death, just a millisecond or two after theirs. Nothing better than joining a 10 mile DME arc on a TACAN approach, descending through 8,000 for 3,000 at about 7-8,000 feet per minute and 50 degrees angle of bank because both pilots decide they want to be heads down in the FMS while we're in IMC conditions. And to add to the scenario, the pilot flying was one of our senior instructor pilots in the squadron.
From the system and performance knowledge standpoint. I pride myself in going toe-to-toe with any one of our aircraft commanders in the squadron. If they beat me in the knowledge, it's an opportunity for me to learn something.
I've had a similar conversation in the past with another member of the board... And while I understand the other side of the argument, I would say that there is a complete misunderstanding from that other side of what a flight engineer really does.
/rant
So... What would be the harm in allowing a FE that meets the requirements of 61.159, with the inclusion of his 500 FE hours, give a shot at an ATP check ride? I would say it would be his pink slip to accept if he truly can't perform to the ATP standards. But, why deny him a chance to prove PTS standards just because you don't think FE's can cut it?