Yes, it's the exact same process, only it's easier with a piece of furniture. However, this should probably not be your first attempt at upholstery, tufting takes practice to have it come out correctly.
The only way the old covering would be of use to you is if you use exactly the same kind of leather, and exactly the same kind of filling. Leather, if it is soft and supple, would actually be to your advantage. The older leather was a lot stiffer than it is now days. It's a lot simpler to do now days having a nice consistent piece of foam to go over.
The depth of the tufts is only dependent on the thickness of the foam you use and how tight you pull the button strings.
No one lives forever, the trick is creating something that will.