I accidentally sent my Explorer on a quest when his happiness level was 10%. Now even after 22 hours he is still at the same level. My doubt is whether I have spoiled his otherwise successful quest. Pls clarify!
I actually did explore this recently, and short answer is no. Dweller happiness only affects your "Weekly reports". It has no effect on production, a dwellers SPECIAL, or wasteland expeditions. (This was part of my experiments to find what increases dweller happiness).
I tested this by choosing one of my most successful explorers, and placing him in a room full of corpses (his happiness plummeted from 100 to about 15 in a minute flat) then stuck him out in the wasteland. He was out there for his usual time (~1 day) and still came back with some good loot - it was actually the first time anyone returned with any Legendary items (got a Legendary recipe).
Needless to say I pampered that poor SOB as soon as he stepped inside the Vault.