My simplest and most straightforward answer to that question is "No, never", not in the sense of traditional dog training. 

Even purely operant trainers use well planned "environmental corrections" to shape a dog's behavior.  An example would be this:  A puppy wants to get up on the kitchen counter because all kinds of goodies can be found there.  Just one reinforcement such as stealing the just cooked pot roast right before the family sits down to dinner will strengthen the behavior of counter surfing to the highest possible level.  Perhaps the next time a puppy surfs the counter, he'll steal a bottle of prescription medication that could kill him if he eats it all.   You can't watch that counter enough:  management always fails.  Instead you put something tempting on the counter and pile up a fragile tower of empty aluminum soda cans full of pebbles, so when the puppy goes to steal the goodie off the counter, the cans rain down on it, scaring the daylights out of it.  If this is its first counter surfing attempt and the shower of cans is dramatic enough, one such environmental punishment will probably convince your dog that the kitchen counter is to be avoided at all costs. 

An operant trainer would argue that you raging into the kitchen, screaming NO, grabbing and shaking the puppy by the collar is not a very effective way to modify its counter surfing behavior in the way you intend.  For one thing, your timing will not be adequate.  The cans fall the instant the puppy attempts to grab the prize off the counter.  You, on the other hand, look up and see the puppy grabbing the prize, haul it down to the kitchen floor and start to eat it before your brain engages your mouth and arms and legs.  You've just completely lost the opportunity to apply negative reinforcement to the puppy's counter surfing--Ian Dunbar tells us that a punishment must occur within 1 second to suppress a targetted behavior.   So instead, the puppy learns that you go into a rage when it is eating something.   But you don't do that all the time.  Sometimes you coo and say GOOD DOG while giving it food and sometimes you say nothing but just plop an entire bowl of it on the floor. The puppy certainly learns that you are unpredictable and inexplicable around its food.  The puppy may have a superstitious response, which is to think it can't eat food off the kitchen floor.  It might then race with the food to someplace else where you have encouraged it to eat food.  But instead , you now scream and run after the puppy and catch it and take away the food and shake it and say "You KNOW you are not supposed to take food off the kitchen counter!" which of course the puppy doesn't understand because he doesn't speak English.  The puppy might at best learn not to counter surf while you are in the kitchen. 

By using ill-timed corrections that you apply yourself, you are teaching the dog a number of things you probably don't think you're teaching and you surely do not want to teach it if you want to train a dog in agility.  First, you're teaching your dog not to trust you.  You teach your dog that you direct bizarre and unpredictable unpleasant behaviors toward it. You teach your dog to be afraid of you.  You teach your dog that violence (yours) is a way to solve problems.  Some dogs will be so afraid of you that they will not return violence, but other dogs will decide to take the other "Fight or Flight" choice and respond back to you with violence.  As Patricia McConnell advises, you can't win a dog fight so don't start one. 

From a training perspective, the problem is almost always that you apply the correction way too late, simply rendering them ineffective as a tool to modify your dog's behavior in the way you intend.   In other words, you end up teaching your dog little else than to distrust and fear you.  Luckily for you, your dog will love you anyway.

Karen Pryor wrote a brilliant article in the first issue of the British magazine, Teaching Dogs.  It is entitled "Poisoning the Cue." which succinctly describes the problem caused by mixing rewards and punishment in operant training.  The gist is simple:  You start out training your dog a behavior by teaching your dog that a cue (stimulus to prompt the dog to perform that behavior) predicts that a reward is coming.  Then suddenly, you decide that the dog "knows" that cue-and-correct response and the first time the dog does not respond to the cue with the correct behavior you "proof" by applying a punishment.  The dog has just learned the cue is now unpredictable at best.  The same cue used to predict a reward and now predicts a punishment. Because punishments must be avoided, the dog now is confused how to respond to the cue.  Eventually if you proof enough the dog now understands the cue to predict a punishment as often as a reward.  Your dog probably does not completely understand what criteria you are using to distinguish which times the cue predicts a reward and which times the cue predicts a punishment.  You are now making the gravest training error:  Your behavior toward your dog is completely inconsistent.

Without applying any value judgments on whether training a dog with punishment is humane, mixing rewards and punishments results in ineffective training at best and it undermines your relationship with your dog at worst.  There is no place for punishment in agility training. 

Even the most traditional of dog trainers seem to agree with that concept in a sport that you cannot make a dog do.  But what is "agility training"?  Does that mean you do not correct your dog just in relation to its fluency on the equipment?   The dog doesn't see it that way, and actually neither do you.  In an agility setting you still expect your dog to come when called, sit and down on cue, just as you do away from agility.  I assure you this:  If you routinely use corrections in training outside of agility those poisoned cues and distrust you've built with your dog will follow you and your partner into the agility setting.  Use of punishment anywhere and any time in your dog's relationship with you will haunt you in the agility setting and interfere with agility training.

Importantly for the foundation class, use of punishment at any time or place in your relationship with your dog will cause your dog not to offer behaviors. After all, if sometimes a freely offered behavior earns a reward and sometimes earns a punishment, and because of your inadequate timing, your inconsistency, and your ambiguous use of cues, the dog truly does not understand  how to know when a reward or punishment is coming.  Because doing nothing results in no punishment, that is the choice your dog will make. Some trainers like that.  They want their dog to wait patiently until they tell it what to do.  Fine. But that eliminates an enormously important tool for training dogs in agility.  Most of what we teach then will depend on their willingness to offer behaviors.  You use punishment, you lose that. 

If you haven't already, please come over to the other side:  Be kind to your dog.  Live in peace with your dog in the R+, P-, E realm of dog training.