Not directly, as far as I know. A fulfilled competency is as much a reward as a badge is, technically speaking. You could connect both to a single activity though:
Upon completion:
- reward badge X
- mark competency Y as completed
It's a bit of a fuss, because you'd have to manage this construction in 2 places, but I guess it's the way this works in Moodle at the moment (unless someone has another idea).