Good point -- if it's one of the handful of Lycoming gasoline engine DA42's (the "L360" model), the issue would not arise. Not sure how many of each of the three different engined models are out there, but I think the vast majority are single-lever power control, so do check to be sure before you fork over any money or otherwise commit to any school. As for the single-engine climb issues above 6000 feet with the L360 model, that's not a barrier to training unless you're in Denver or Salt Lake City or the like, and it will better prepare you for the realities of flying most light piston twins.
Considering most ME additional rating training is conducted within about 15 miles of the airport, I don't think that will be a issue.
No fun getting up there on the test, doing the shutdown drill, and then having to discontinue the test and land incomplete because the prop wouldn't come out of feather, and you will have to do that at least once in training and on the practical test.
Why would you have to disconinue? If you landed anyway with thte engine shut-down, doesn't that fulfill what the examiner needs to see? But I am glad my examiner heeded my advice to not shut down my right engine, which I knew had a bad accumulator and starter since I had to land twice with it completely dead...
If every one of the required Tasks were complete except that one, then yes, I suppose it could work. But usually, that won't be the sequence of events. Otherwise, they'd have to do a bunch of airwork, then do all the takeoffs and landings (no examiner is going to be happy doing the single-engine instrument approach or engine failure after liftoff until s/he's seen you operate one-engine-inop at a safe altitude), then climb back up above 3000 AGL (or higher, depending on what the POH says about safe single engine training altitude), do the shutdown, and descend for the single-engine landing. That's just not the sort of plan of action I've ever seen for a multiengine additional rating ride.
Most ME trainees are getting the rating to fill a square and then move on to some ME flying job. There aren't that many doing it so they can rent the twin they trained on. So, as was stated above, if you're going to be flying a single-lever TwinStar (either rented or purchased) after you get the rating, that's a good choice, but not otherwise.
While it is true that most folks getting a ME rating are doing it to move on to a professional flying job, very few are going to get hired with a wet multi-ticket and 10 hrs or so of twin time. Usually have to build some ME time first in order to meet the hiring mins.
