I was in middle and high school when calculators became the standard, but they were still expensive enough that we kept the Ti-80 calculators on a backroom shelf and checked them out when there was an overnight problem set or homework assignment. In a round about way, I think I ended up understanding more about the underlying maths because of this.

So, no, many did not actually learn arithmetic in school. This isn't necessarily because of the calculator, but if you don't get a student to understand what arithmetic even is then handing them a calculator may as well be like handing them a magic wand that "does numbers".