You may certainly be correct, but part of your viral coefficient is likely driven by continued usage of your application. As such, I guess there are two ways you could go about it:

1. Spam user's social network on sign up; 2. Send out periodic blasts about progress/offers as the user continues using the app.

The first method will likely net you terrible reviews and negative sentiment, while for the second, an exploratory mode wouldn't really hurt you. The key would be designing exactly when and how the sign up should be. For example, maybe after 5 days or 5 app opens (whichever is more), the app loses functionality until you connect. It'd be different for every app. For games (or gamified aspects), you could just incentivize sharing.