Does standing up while pedaling increase chain wear (lengthen chain) faster than pedaling while seated?
The amount of force required to plastically deform a steel chain is much more than a human can exert, even if you embedded the rear wheel in concrete so that all the force went into stretching the chain, rather than turning the wheel.
Chain "stretch" is 100% caused by wear, with grit in the chain grinding down the rivets and sideplate openings. Standing up to pedal has nothing to do with it. If the chain is dirty and its parts are moving relative to each other, the parts will wear down.