I don't know anything about flying turboprops, but the following applies to jets.
We have a simple phrase for 3 engine ferry ops. "Good engine, good wind. Bad engine, bad wind". This means you want the wind coming from the good engine side. If you're taking off on 36, and have a crosswind from 090, you're going to use some of the rudder to keep it going straight. The more wind, the more rudder. Now, if the right engine fails, you may not have enough rudder throw left to keep it on the pavement.
Once it's in the air, it makes no difference.
Bellophon-
>>, any engine failure immediately after lift off was significantly more difficult, and rarely as well handled, as an engine failure immediately after V1.<< I see this all the time. Two reasons, I think. 1. The lack of visual clues. 2. Most pillots have had quite a bit of practice with V1 cuts, and are expecting them in the sim. Once airborne, the mind set is "OK, no V1 cut, so it will be a normal climb out". A V2 cut at 200 agl comes as a big surprise.