I can share the personal observations that I've noticed.
When I'm mentally stressed (remember, I'm an engineering student), I go to the range to blow off steam. The first few shots I fire off are almost always terrible - not even close to the target. As I clear my mind more and enjoy why I'm there, I tend to do better. Say I get a phone call that upsets me - I'm back to square one.
From what I've seen, a friend of mine was shooting in a pistol competition for the state championship. He did great the whole way through, until the guy who covered his entry fee (since he didn't have the money to enter himself) got DQed for something miniscule. At the very end it bothered him enough that he didn't quite do well enough to take 1st. I don't know if this classifies as "stress", but being mentally upset by something seems to have a difference.
Physically? I don't think so. I could go a while without sleep, and as long as I still get the adrenaline rush of shooting, I'm okay. 5 hours after being out at the range and shooting 12 gauges, I can still shoot as well as normal with a pistol. In fact, that's what happened with my luckiest shot of all. After a day of shooting shotguns and rifles and feeling quite physically tired, I put up a 12"x12" target at 50 yards, loaded my last round of pistol ammo in my gun, aimed a little high, and hit in the 3rd ring of the target. Pure luck, but the fact I didn't limp-wrist is impressive enough (I've also broken both my wrists several times, hehe...)