[Editor: A bit of google research gives the answer as a clear "no". The only way tail-less mutations arise in nature is spontaneously by chance. Breeders have then taken these rare tail-less mutated dogs and bred them with other kinds of dogs, then mated their progeny with the same kind of dog to introduce the gene to the breed. It's all because of human breeding and it has nothing to do with docking tails.]
Absolutely correct. Cutting the tails off has no genetic consequence, there is no way for this action to cause a change or a selection to the animals blueprint (genome carried in the gonads).
On the other hand, if one did selectively breed the parents of animals that gave rise to occasional animals that had shorter tails (that is to say, shorter tails when they were born), one would have a good chance of selecting a breed that had fixed (made homozygous in genetic terms) a mutated form of a gene that lead to shorter tails.
This process is the basis of most (maybe all) animal and plant breeding as it has been carried out for thousands of years. Animal or plant breeders really do not have to understand genetics to use it. They just select and breed animals that have the trait they want to enhance...... Of course the trait has to have been based on a genetic change for it to be sucessfully fixed.
For example, selecting for short stature in a population of poorly fed people would not necessary select for shorter people, since many people may have been shorter because they did not have abundant food at the time they were growing quickly. There are mutations in most mammals with tails that result in tail-less animals. As I recall the mutation is not a really useful one because it is lethal (causes the animal to die) when homozygous. It's not great having a breed where 1/4 of the progeny die.
There may well be other mutations, other than the one I refer to above, but I am not aware of them.
So, according to genetic orthodoxy and 100 years of experience, repeated mutalation of an animal does not lead to a genetic change mimicing the mutilation. Consider the case of circumcision, practiced for 100s of human generations, and so far it has not worked at the genetic level.