Your net elevation change is just the difference in altitude between your starting point and your ending point. So yes, it’s independent of route, but that’s not what the term “climb” refers to. It’s not a net elevation change; it’s a cumulative elevation gain, because in bicycling and walking the in‑between parts burn energy. Human legs don’t have regenerative braking, so every time you gain a foot of altitude you don’t get those calories back when you lose a foot of altitude.

Not if there are hills in between. But the delta between A and B is the best you can do, yes.