Can my cantilever brake pads not being centered lead to a problem?
On rim brake calipers the cable pulls the two sides towards each other to 'pinch' the rim. If one pad contacts the rim first it will not exert any significant force until the opposite pad contacts the rim.

Centering the calipers allows the distance between the pads and rim to be minimized, thereby reducing the distance the lever has to be moved before braking force starts to be exerted.