There's probably enough leeway there for the government to construe widespread defacement of bills with adverts for competing currency as illegal. I wouldn't try to start such a movement, more likely to attract the kind of attention bitcoin doesn't want.
The fed don't need to take up any "leeway" they gave,
advertising on money is illegal. OP is 100 years too late to the idea of putting advertisements on US money. Somebody already annoyed them enough they made a law against it before we were born.
I was sure that was the case, thanks for digging up the statute.
I'd estimate this idea has a negatively assymetrically skewed expected payoff for bitcoin as a whole, better to shelve it and come up with something else that doesn't directly antagonize governments.