Historically, I read somewhere that the whole point of everyone wearing a robe at a graduation ceremony is to put everyone on the same level, i.e. make it impossible to determine someone's wealth or social class by the clothing or jewelry they wear or don't wear, etc. The point is to make everyone look uniform. If you're graduating with academic honors, then great! Absolutely wear a stole or cord or whatever. Anything beyond that is too much, I think. But that's just me.
However, I think wearing your badge underneath your robe, or even on your robe (because they're usually pretty small) would be okay.
