The track may have been lifted, but the points that provide access to the Bridge Street line are still there, and still usable - they're certainly not clamped out of use. The signal at the south end of platform 1 (the usual platform for up departures) still has the capacity to signal out onto the main (by showing green with a "U" in the theatre box) or onto the branch.
The line does indeed head out towards Brackmills - in fact, there is/was a Geismar plant that was accessible by rail. Somewhere in the depths of my memories, I can remember an 08 ambling across Bridge Street and heading off towards it. I believe (although it's possible I'm wrong) that the new uni campus which actually be on the site of the old Power Station - so, just in front of the old trackbed. Looking at Google maps, the track only actually exists as far as what was the Geismar plant. Beyond that, Brackmills (and the A45 Nene Valley Way) are built over what was the trackbed.
Much as I'd love to see it, it would be a hell of a job to re-instate it now. Most of the villages along the A45 such as Billing, Earls Barton, Castle Ashby and Doddington actually have a "Station Road" where you'd never know there was once a station.
Some information can be found at the following link.
http://en.wikipedia.org/wiki/Northampton_and_Peterborough_Railway
