If I send a dweller out to explore. Does she still consume food and water which I produce.
As an experiment, I sent every capable (ie not pregnant adult) out into the wasteland to watch my food intake. Of course there was still a bit (because of said pregnant dwellers and children) but it was dramatically reduced. I later used this as a tactic on several different occasions where I was running out of food or water. I had the pregnant women manage the food/water/power production, and as it started to build back up again, I'd slow recall the less-capable (ie will die soon) dwellers back to the vault.
Edit: I should point out that this is a very dangerous thing to do, for if radroaches or raiders attack, my vault is not defensible at all. I took that chance rather than have my dwellers starve.
As near as I can tell, no. At the very least they aren't harmed if you're not producing enough. During one self-inflicted crisis where I was struggling to get production balanced, I ran out of water for an extended period. My entire populace at the vault ended up suffering around 50% radiation sickness and their happiness fell to 10%. The one vault dweller who was out exploring at the time didn't suffer any radiation sickness and her happiness remained at 75%. So it doesn't appear that they consume any food or water.
In additional confirmation to the other answers, I have another supporting data point. I was just on the edge of critical levels of water when I sent a dweller out of my 16 member vault. As soon as they left, the water levels jumped from red to green, without any additional production.
I'm using Fallout Shelter on PC. I don't know about the mobile version but I get stats including resource production and resource consumption. Let's experiment. I already have every non-essential dweller out of the vault right now. This means only primary resource producers are still here. I will give you the stats of my food and water production at current, then I will send out a power plant worker and give you the new stats.
ALERT!! RAIDER ATTACK IN PROGRESS (EXPERIMENT ON HOLD)
ATTENTION PLEASE: THE SITUATION HAS BEEN NEUTRALIZED. PLEASE RETURN TO DUTY.
Production/Consumption levels unchanged. Lets send out a level 10 Power Plant worker.
The vault is now consuming 0.36 less resources. Lets remove one more to see if that's typical per dweller or if level has anything to do with it.
Sending out a level 4 Power Plant worker
New consumption falls to 6.12 making it another drop of 0.36. This means each dweller sent to the wasteland consumes the same amount less. Hope this helps.