Probably not. According to their site, GeoIP2 is not a "new version" of GeoIP; it's a paid web service they're offering in ADDITION to GeoIP.
So basically you can pay for the privilege of doing the exact same thing you're doing now, just more slowly because all of the lookups have to be submitted to their API server instead of being handled locally on your own server. It doesn't seem like the best value proposition from my perspective, although I'm open to other opinions.