Of course it does something in this instance. Otherwise the light would never change to the barely-used crossing.

There’s a pervasive myth about elevator buttons and crosswalk buttons being there as placebos. Yes, I’m certain there are instances where—when the traffic lights regularly cycle all day long—they might be placebo buttons, but the vast majority of them will at least lengthen the cycle time for your direction, and if appropriate will trigger a change sooner than it would have occurred otherwise.