That's not entirely true. While fuel injection would work, a diesel at a high angle of heel with a sump would likely circulate its oil unevenly, and would, unless using a universal coupler, likely start to wear the transmission and the shaft as it went out of alignment as the weight of the engine unequally compressed the motor mounts.
In a survival situation, this isn't an issue, but running the engine while heeled isn't, to my knowledge, a great recipe for longevity.
This is why I mostly sail, or motorsail in light air, or motor directly into the weather if I have to go in that direction. The fore and aft motion is easier on the tranny than going from 40 degrees port to 40 degrees starboard.