Pete,
Yes it does smoosh the backgrounding a little, but you can just touch it up after you are done beveling. And the beveling is there, but since you run the backgrounder over the beveling, it masks it.
I might also add, this is how I teach it to beginners to get them to learn to follow lines. If they jump a line, its much easier to cover up the mistake before beveling. Nothing is more annoying than seeing a tiger cub in tears cuz he screwed up and can't afford the $50 for a new piece of leather (That's a story for another day)
Once the skill is developed, you can do it in any order you want. Personally, I bevel first then background because you get much more depth.
You will find also if you bevel first your backgrounding goes much more quicker.