When you mix egg whites with sugar, does a chemical reaction occur?

It does if you use a copper bowl.

There is a chemical reaction between the copper bowl and the egg whites that lowers the pH (or acidifies the whites) and gives the beaten egg whites a better texture.

Scroll down to copper cookware.
http://www.gourmetretailer.com/gourmetretailer/magazine/article_display.jsp?vnu_content_id=1000741975

"The ability of reducing sugars to react with amiones as well as basic amino groups of proteins and nucleic acids without enzyme mediation is a phenomenon known as nonenzymatic glycation"

Known as Maillard's reaction, it can occur both in the test tube and in the body and is thought to be behind the pathogenesis of diabetes among other things (where glucose and albumin are together in a nice warm environment and can happily react together whenever they like)