The drugs necessary to tranquilize or anesthetize animals are controlled substances. In Canada they can only be used under the direct supervision of a licensed veterinarian.
Some of the drugs used for darting large game species like rhino's are extremely dangerous to humans. The volume in a dart is limited so the drug needs to be pretty concentrated to knock out a 2000kg animal.
Etorphine (Immobilon) is such a drug. The instruction manual specifies that you have to draw up the antidote and have a person trained in giving intravenous injections standing by while you load the dart. This drug has killed a few veterinarians in England when they got a drop on their skin or in their eye.
http://en.wikipedia.org/wiki/Etorphine
The effect of the drugs can vary quite a bit from animal to animal. First off: you cannot weigh them, so their weight is always a guess. Secondly there is individual variation to the effect of the drugs. Same in people; some get giddy after their second beer, others not until their fourth sixpack.
Some animals appear tranquillized until you get near them or touch them. This provokes their fight or flight instinct and that could make for some exciting photo ops...
If the animal dies, either from stress or overdosing, the meat is unfit for consumption and should not be left in the woods as it can endanger other wildlife. There are several reports of eagles dying after eating the carcass of euthanized horses.
To return to the topic: I have been on many hunting trips without killing anything. In fact, usually I do not even see deer on those trips....
