> You will not pick up multiplication from using a calculator

Sure you will, at least assuming we're still talking about memorizing multiplication tables here and not how to do long division or the like. I don't think algebra or even basic calculus has any convincing need to involve rote memorization.

I've ended up unintentionally memorizing many things due to frequently needing to consult various lookup tables.

> conjugation

Competent ones will. Wrong conjugations usually "sound" wrong to me even when I haven't seen them before and that's in English of all things.