Lots of dog's owners and even trainers will tell you, it is not possible or not good enough if you take on competitive obedience with positive training. Especially when you mentioned clicker.
But I see it from a different perspective. My dogs are eager to do I want them to do, and they did it happily. That should be the spirit and purpose of O.T. The enjoyment of the dog Sports and exhibiting the usefulness of dogs.
We've much success with our full clicker trained Aussies - Keesha and BC - Benji. They are so successful in O.T. We've both cross-over dogs, BC - Max & Mikah too. All doing superbly well in O.T.
Clicker Trained Dogs are thinking dogs. Here are the following reasons why I strongly recommend reward-based training techniques? 1. You don't need to be dominant to be successful, 2. Your dogs are always thinking, 3. Your dogs are never afraid to try new things, 4. Your dogs are very creative, 5. You have a Very Happy dog, 6. You are always more interesting than others, 7. Your dog loved every second of its time with you, 8. You have its trust & respect 100%, 9. You are always rewarding rather than punishing your dogs, 10. You will have a very reliable dog. Hope all these reasons can help you re-assessed the value of reward-based training technique.