TC well done for downloading the FAA doc - I baulked at 20 mB and an .exe file!
Anyway, it is interesting:
By lowering the collective pitch, which must be
done immediately in case of an engine failure, lift and drag
are reduced, and
the helicopter begins an immediate descent,
thus producing an upward flow of air through the rotor
system.
Note my different emboldening to yours. The statement is reasonably true when flying at modest speeds, or even flat out in a Bell 47! However it fails to take account that at high speed (by which I mean a modern heli doing 150 kts) the small pitch change that results from the collective being lowered has a huge impact on the g loading. Yes it makes the helicopter descend rapidly, but it does not produce an upward flow of air through the rotor system, at least in the short term.
So in fact that document is wrong, probably outdated from the days when helicopters max speed was not that high - the technique probably worked then.
You say to maintain the attitude, yes I can go with that, certainly better than just dumping
the collective. But a slight pitch nose up will result in less reduction of Nr compared to maintaining the attitude. My point is that this last thing is the most critical, especially in a twin where double engine failures and the need suddenly and unexpectedly to have to enter auto is a much less than once in a lifetime event. There is a good chance of being stunned into inactivity for a moment.
First priority is to keep the rotor rpm in a flying range. If you fail at that first hurdle, you can forget a landing zone.
Yes, once that is in hand, the second and much lower priority is to choose a good landing site and try to make it. But if you get that bit right, but not the first priority, you are wasting what little remains of your life.
Put simply, flaring the aircraft slightly increases your chances of surviving the unexpected auto entry and that is all that matters. (all this of course from cruise flight)