AWhat happens to the extra icing one has laid down on the parchment paper which extends outside of the edges of the traced circle of the appropriate sized pan? Does it get scraped off during the application of the icing to the sides?

Yes.  I use a bench scraper to smooth the icing on the sides and the nice sharp edge easily takes off the excess that is on the bottom (or top, actually).

AThanks for responding! I'm going to give this method a go with an American buttercream recipe this week. I like to obsess over details well in advance and freak myself out. :)