I would do it for sure. Most people probably wouldn't care about the links traffic being public, but they will be turned off by a registration process.
That would make me not use the service. If I'm short-linking on my blog or Twitter account, I want to know that if someone clicks that link 2 years from now, it will still function.
I actually would be curious to see how many people clicked it (and when) and I usually wouldn't care if other people saw it as well.
