Yes. The process teaches you how to think logically and about how numbers work. Calculators short-circuit the process, providing answers without understanding.
Exactly. The underlying reason for HOW and WHY these techniques work is what's important. I will never forget ( or forgive ) a teacher I once had who told us when explaining recursive algorithms that they were very important, and to MEMORIZE them, because we would use them, but don't bother trying to understand how or why they work!
Mark