Neither Navajo nor Chieftain is my favourite piston twin. I was told by a very old hand in the game that if one got low and slow in a Chieftain, do not add a little power, add it all, as the time taken to overcome the drag and accelerate is much greater than the time to decelerate to VMC..., or some such.
Once you are single engine below blue line in any PA31 you will probably need to trade altitude for an increase in airspeed. The aircraft develops very high drag below that speed and is very evident at high weight the time it takes to accelerate from rotate to blue line on two engines, then from that point it pretty much climbs at the same rate for the next 40 kts.
If an engine fails early on below blue line you are in a very nasty place, however with two on board (assuming no freight) it should be able to accelerate if the aircraft is cleaned up fast. This all depends on what rotate speed you use and what sort of terrain you have to accelerate over.
Windmilling prop and you have no chance of climb.
Last time I did training in a PA31-350 we had 2 on board, full fuel and ballast and the aircraft climbed at 500fpm on one engine on an ISA +5 day.
I know directly of two occasions where a chieftain engine has failed just after take off and the pilot has managed to climb to circuit height and return for a safe landing. Both with more than 2 on board in ISA +10 or worse.
the poor old thing was still descending in the go-round 2 out of 3 times at training weights. Pilot mishandling... not likely.
This shows a big problem with the particular aircraft if it was not pilot error and the aircraft did not eventually climb. The reason for a single engine committal height is so you can use that altitude to clean up and accelerate back to blue line and climb away. If you are below that height you land no matter what due to lack of performance.
Full power on the Navajo engines is regulated by the density controllers, if these are not adjusted regularly for seasonal atmospheric changes you could be running at far less than maximum power at full throttle. Also small things like the rigging of gear doors can have a big influence on performance so good maintenance is essential.