Works on an A330 at MTOW, guess it would depend on the engine or engines you lost on an A340 and your speed, having not flown one I could not comment. The Airbus instructor’s manual indicates it should work on the 340 but if you have tried it in the Sim I will take your word for it.
Yes it is a function of normal law but that’s the point the aeroplane protects you all you have to do is step on the correct rudder to improve the climb rate which at MTOW won't be very good if you don't centre the Beta target, which is perhaps what you are alluding to.
Using the spoilers and aileron alone is of course not an approved technique and I would not suggest otherwise. My point is you have another level of protection that would not be available on more conventional aircraft.