In my opinion is just a fairy tale. Anything that hurts the tree significantly will trigger flower production instead growing wood, but there is a price also. The price is measured in years of life and health of the tree.
Cons: Damaged bark, open wounds welcoming entry of fungus, and nails that can hurt you. There is a risk to catch a brush cutter or scratch your feeth in a nail.
Benefits: My father did the same a lot of years ago in an lazy seedling orange tree. Nothing changed. He has to wait still the same 10 years for their first orange than with a standard tree. Eventually the tree started to produce and currently it gives fairly big harvests each year. Sometimes after a big season is chlorotic and need chelates like any orange tree... And shows two ugly useless nails at the basis. Another orange tree without nails that I planted close behaves exactly the same.
In my experience the benefits are unclear and probably zero and the risks are clear. You can achieve the same with pruning
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Second question. You must assure that everybody working in your place has been vaccinated against tetanus. Be careful also with your dog, pets love to dig and vet bills can be expensive.
I thing that there is a better way. Steel balls would be much better than nails for your experiment IMHO, You can find plenty of it in any garage near to you or in a car scrapping. They are totally safe for paws and hands and (after cleaned of its oil) will rust and blend with the soil like a pebble, so are much more pleasant to see also. Let the nails for furniture only