I partly tested this on a mission where a UFO landed (rather than being shot down).
I dealt with the aliens immediately outside the craft first, then saved the game. First attempt I went in slowly, room by room, killed everyone and got the loot. I then reloaded, and rushed my team to the room with just the last enemy - avoiding two rooms in the ship which contained working ships navigation and working power core. At the end results screen I still got those despite those rooms still being covered by fog of war.
Maybe not the most comprehensive test of the exploration, but I think so long as you either kill all the aliens present, or otherwise complete the missions objectives you get everything.