Some thoughts .. (caveats - no free turbine piloting experience, only F27/L188 and not speaking specifically to this particular aircraft loss)..
Many have disputed this from their own hands on experience, yet some continue this "windmilling prop / no climb theory".
The certification basis will give you the starting point for figuring what might or might not happen given this or that problem.
In general, if the weight is (appropriately) low enough, there ought to be no great difficulty climbing with a more adverse than certification thrust/drag situation .. not much different, really, to the similar problems with light twins in a takeoff engine failure situation ... hot and heavy = forget it ... light and cold = far less sweaty.
The principal flight management problem with this sort of training manoeuvre lies in handling qualities and consequences of uncommanded/unexpected failures at a fairly critical stage of flight. If a failure-related problem occurs, say, around or especially a little below V1 with a near Vmcg/Vmca limited speed schedule, and the takeoff is continued, then things might rapidly get out of the pilots' ability to keep on top of the situation. The propeller beast is far more critical, in this regard, than its turbofan brother.
So far as what the failed engine's propeller should do, generally we see the certified system's incorporating either autofeather or neg torque sensing to drive the failed engine's prop to a pitch condition resulting in a predictable (reasonably low) drag so that handling problems, initially, and climb capability, subsequently, are manageable and within the certification expectations.
In my type we brief to climb to acceleration altitude (400 feet AGL) with a windmilling prop (NTSing), T/O flap and gear retracted.
which is the typical certification scenario .. where the handling and performance is predicated on autofx/NTS correctly functioning
The only time we will feather the engine straight away is if we have an NTS failure in which it will happen as soon as the gear has been selected up.
.. (or autofx failure, as appropriate), either of which can be expected to result in a critical situation generally requiring fairly rapid pilot response to maintain control of the situation
There are many school of thoughts that it's ok to fail an engine before V1
.. provided you intend to stop .. especially if you are on a near min speed schedule
There's no reason the a/c cant be configured to simulate an EFATO at 2000 feet
.. perhaps not really a useful training consideration generally for heavies ... however, a good strategy for initial failure introduction to a multi engine new chum.
Who the hell is going to do this at a few hundred feet AGL as their aircraft is rolling and descending - I doubt I would.
.. been in a similar situation in the 727 sim engine failure with the FE being a bit slow on the old "check essential" thing (long time ago so I'm stretching the memory a bit) ... either way we ended up with no rudder for a bit and the thrust had to be reduced substantially to give us time to catch up with the FE's delay.
In the real world, it is a matter of discipline and training ... leave the power on you DO die .. inverted. Pull the operating levers back a bit and you MIGHT just live in the belly landing. You might well doubt that you would .. I doubt that I would not ... when you have departed controlled flight without a preprogrammed recovery, the normal rules go out the window and you are looking to maximise the probability for a survivable accident.
So far as training in the aircraft versus training in the sim, the sim is preferable if you have a reasonable fidelity device available .. you get to have the other guys smile and chuckle at your mistakes but you also get to have another go at getting in right next time around.
Having said that, some training ends up needing to be done in the aircraft due either to no sim being available or inadequate sim fidelity for particular requirements. I did all my F27/L188 training in the aircraft but with fairly rigorous adherence to published protocols. Even then, some silly things were done eg for my L188 endorsement - it was all done at night due to aircraft availability and with non-flying pilots standing in the cockpit observing. I shudder now at the likely headlines had something gone wrong .... however, we didn't do overly silly things like training at near min speed schedules.