there is part of the flight envelope where the take-off could be fairly normal if rather long followed by no spare performance for any additional climb
Not really; once you are out of ground effect and flying OK then the thing should carry on flying. It might climb very slowly (of the order of taking 10 miles to climb a few hundred feet) but it won't crash.
Unless the pilot pulls up a bit too hard (remember that this plane was very likely substantially overloaded) in which case a flight slightly above Vs can turn into a flight below Vs.... or there is a loss of power.