I can believe that the growth was significantly helped by third-party clients, but I wouldn't believe that the more creative twitter integrations had a major effect. That would be a dev/techy-centric view of the world, similar to those that truly believe that the real-name policy was a mainstream issue that killed G+.
When I started on twitter, it had no hashtags, replies were public (because they weren't initially part of the protocol), no t.co, no embedded photo sharing, no geotagging. All of these features were added, and made popular, in third party clients before being added to Twitter. It was like a giant lab where the features could be tried by smaller groups who shared certain clients or norms and the popular ones wrapped into the "official" API eventually.
