The middle pedal of a grand piano is called the sostenuto pedal. Its function is not as you describe; the way it works is that it holds off the dampers of the notes that are down at the time it is depressed. This enables you to hold a note while still pedalling normally to control others (it can be used for that in the central section of Debussy's La Cathédrale Engloutie, for instance, to make the chords less muddy while continuing to hold the big bass note representing the bell), or it can be used to hold the dampers off a number of notes which have been pressed silently so that subsequent playing leaves resonances of those notes only. The second usage is quite common in contemporary piano music, of the sort my son (a concert pianist) tends to play.
I have heard of the mechanism you describe as a rarity on upright pianos, though, but I've never seen it.
Either way, I can't think of any way you're going to be able to capture the sound of the resonance without the sound that excites it, though. I suspect the best you could do would be to record the result of playing individual notes and chords and then to edit the later parts together as a separate exercise.
