From a US perspective too, listing a 1000 rep is unlikely to be helpful. Something that goes onto your SOP should probably involve hundreds of hours of dedicated work; it should be hard and compelling. Perhaps you could weave it into your technical narrative-- listing a discussion you had here that is particularly relevant to the rest of your SOP.
Academia.SE would probably not help at all, unless your PhD was centered around education. I would suggest that you weave it in only if you can find some posts which were significant contributions on the Electrical, Computer Science, Math, Physics SE (basically the area of your PhD).
Most programs do allow you to specify a web page (though these are often ignored). If you're planning to include one, you could add a SE flair and link it to your SE network profile.