Yes, you can carry over the shoulder. In my opinion, in carries better than traditional stud locations.
I'm right handed. I like the forward cup on the left side of the forend and the rear on the right side of the butt. It works great with a bino harness being carried across my chest while having a pack on. It carries on my shoulder as well with a pack on as the traditional location in my experience. Added advantage, if you remove the sling you don't have things poking out from the stock to snag.
@SDHNTR traditional sling studs and the rifle at ones side as the gods intended is uglier than a lobsterback in Boston and for cosplaying larper premadonnas who think they are going to war with the Iroquois.