The projection systems don't favor the Pirates to make the playoffs, and it's not close.
Taking an average of the projections from Baseball Prospectus, Clay Davenport, Fangraphs, and FiveThirtyEight, the Pirates have an 11.2% chance of making the playoffs this morning. That ranks 9th among NL playoff contenders, even after adding Chris Archer and Keone Kela, and even after winning two of three since the deadline.
On the low end, you have Baseball Prospectus and Clay Davenport, both giving the Pirates an 8.2% chance, which either ties or is worse than the Giants in each simulation. FanGraphs is the most optimistic at 15.