Engagement is crazy right now. I drove home at 3am last night and stopped by a PokeStop, and as I was leaving the parking lot, another car pulled in just to play... Same at the church by my place 15 minutes later. Different car.
What will really be telling is how many people still play after a week or two.
I feel that if they don't get the server issues under control soon (I saw they delayed the European lunch) then it doesn't matter what WOULD have happened the game is going to lose players in the social/network effects won't be there.
I think more of an issue will be people hitting "completion" relatively soon. Certainly, the most interesting part right now is just catching new Pokemon, but there aren't so many that you can't burn through most of that enjoyment fairly quickly.
So far the game only includes the 151 original Pokémon, and I imagine it should be pretty straightforward to add in the later generations (700-something total). That's without adding things like shinies, gender, etc.
What will really be telling is how many people still play after a week or two.