Well, just tried doing a locknut open vs locknut closed comparison and I can't feel the difference. There obviously is some stretching occuring behind then nut because if I bend a string, clamp the nut while holding the string bent and then release the string the resting pitch of the string is marginally flatter than when it started. If I then release the locknut, that pre-bent string then returns sharper to the correct pitch.
I made some measurements to see if there was a difference in distance it took to bend a string up with the lock nut engaged or disengaged. The 3rd string was fretted at the 9th position (E) and bent a full step up to F#. For each E and F# I used a Peterson strobe tuner to make sure I was nailing the pitch for both static and bent strings. Calipers were utilised to measure the deflection of the string using the edge of the fretboard as a reference:
Static distance of 3rd string from treble edge of fretboard at 9th position = 21.11mm
Distance from treble edge of fretboard, bending up to F#, locknut off = 34.27mm (deflection = 13.16mm)
Distance from treble edge of fretboard, bending up to F#, locknut on = 33.26mm (deflection = 12.15mm)
1mm difference is about 8% change in deflection required to raise the string pitch a full step, but in practice I personally can't tell the difference; It just gets absorbed into the mechanics of my playing. The deflection difference may be more pronounced if the Floyd wasn't fully floating and was blocked off.