Maybe. It still wouldn't be foolproof - after all, Yelp Check-ins are powered by an API that trusts the coordinates it receives.

It might be possible to craft a request for that API. And even using a legitimate copy of the Yelp app to make requests, a jailbroken iPhone can change its coordinates to whatever you want. An Android doesn't even need that - just set it to developer mode and you're ready to fake check-ins all day.