Hm I think you have a choice as to how you train for such scenarios, and what you choose to carry about with you.
If you take self-defense classes and carry around a more low-profile self-defense tool like mustard spray, a rape siren or maybe even a robust umbrella or walking stick, I think that's more likely to have a better outcome than if you choose to carry around a karambit (especially if you don't know how to use it).
If you get into a knife fight armed with this thing, then you will find yourself fighting knife-to-knife, and as wonbul pointed out, even if you win, you're going to be cut up. On top of that, it's also likely that the other guy will be cut up worse. If you have caused serious injury or even death in the process, you might find yourself facing serious criminal charges.
In that case, this thing would seriously complicate your legal defense. You might find it difficult to convince a judge or jury that you were an innocent victim and not the aggressor when you were walking around armed like a goddamn velociraptor.