Well, we are talking takeoff, not cruise here. So very probably not. Maybe on two, but if they were on the same side, it would take an outstanding pilot and a lot of luck.
I recall the plane in question didn’t have much in the way of cargo, so again, the loss of a single engine shouldn’t have been determinative of the outcome.
Absent facts, I’d speculate a combination of mechanical fault and pilot error.
On take off, climb you are at a pretty low airspeed.
Loss of an engine and torque compensation with rudder further reduces air speed. It looked to me like the left wing simply stalled. Some would ask how only one wing could stall but there are many situations where that can happen. The engine that failed would reduce air flow over the wing on the same side. Once the wing drops at low altitude your done.
The proper course would have been to stop climb and lower the nose to get speed and then at least you go into the ground wheels down instead of burying the nose. It looked like he may have tried that and then tried to correct course with too much rudder, rudder can really kill airspeed.
Thanks, PAR35.