L.M.
My daughter got part of her hair dyed purple at a local beauty school. The supplies to do it at home would have cost more than the beauty school charged. They did a fantastic job. There was no "allergy test" done, but they also weren't applying the dye to the scalp, just to the ends of the hair. I did have to sign a release form.
I do understand the reasoning behind performing the patch test. It's a good idea in the rare event that you do have an alergy and it's possible that it may be a law in your state.
At a good beauty school, everything is closely supervised by an instructor. IMO you should give it a try.