Darkness will probably take less than the last film (about $375m from memory) due to all the fans who didn't like it not giving Abrams another hearing.
When a film breaks big - $700m big - it's the casual filmgoer who is the deciding factor rather than the fans.
And it's comon practise these days for studios to want a sequel to do better than the first (or at the very least match it). Would Paramount pump an estimated $185m into the Trek sequel otherwise? It's in their best interests for them to want it to do as well as possible. It's a business, not a charity.
it's been almost 4 years since the last movie, lots of time for DVD, Blu-Ray and TV showings to shore up support for a new adventure, and there seems to be enough buzz to make it happen...
Plus, I think you're underestimating how much the 2009 film has appealed to non-Trekkies in the time since its release, I know people who can't stand the "geeky" pre-Abrams TV shows/movies but loved the 2009 film.
Both true. The post-release performance and public response will have been instrumental in the development of the sequel.