Yes, this method works for parrots of all kinds whether they are hand tamed or not. The primary reasons that budgies or other parrots do not come to us is because they are afraid of us and don't trust us. The method that I gave you is all about showing them that we are not going to hurt them and that we can be trusted, it also teaches them that we bring them good things to eat.
English or show budgies all have much shorter lifespans than normal type budgies and are prone to more illnesses.
I know that I have recently gone over this with someone that has budgies, but do not recall who it was with, so forgive me if it was you, but it is actually very important for the health of your birds
Budgies can eat more seeds than many other parrots but an all seed diet will destroy their liver just as it does with other parrots. So what do you do, because they really like their seeds and would happily eat only seeds. I would suggest that you start their mornings of with partly cooked wild rice or quinoa or steel cut oats and mix some budgie seed mix into it. I would use about half a teaspoon of budgie seeds to a teaspoon of the cooked food to begin with. And then give then just the budgie seed mix for their dinner. when they are eating the cooked food/ seed mix pretty good then I would start adding things like cooked peas or corn or carrots to the mix just one at a time until they are eating it pretty well and then add the next vegetable. I would also give them both a whole leaf and finely shredded romaine or red leaf lettuce wet. I would place these food on a small paper plate or saucer on the bottom of the cage for them. I would do this way because budgies are ground feeders. Budgies do not usually eat much fruit, I have gotten mine to eat a little bit of finely chopped apple once in a while.
Here is a list of all kinds of things that are good and bad for budgies and other parrots, the list starts on the second page.
viewtopic.php?f=8&t=12521 What is the name of this book and its author about the wild seeds for bird? I would love to see if I can get a copy of it.