Jimmy, the I think the answer to your question is yes, although I didn't use two different amps to check.
When the DS-5R is used with the two patch cords, both into an amplifier input, and the DS-5R Stereo / Mono switch is in stereo, both neck and bridge pickups are heard through the amp, as selected by the bass P/U selector switch: Neck, both or bridge.
Using the same setup, but then flipping the Stereo / Mono switch to mono, only the bridge treble pickup comes through the amp. In this condition, moving the bass selector switch to neck pickup results in no sound.
Although I can't do it tonight, I could try the experiment again tomorrow night using separate amps to ensure that there is complete separation between the neck / bass and bridge / treble outputs. I ran the the patch into two inputs on the same amp, [one input is damped by 15db, so I could tell which DS-5R output was operational due to the volume difference]. However, my notes show that either the bridge or neck was available from the DS-5R bass / mono output (depending upon bass selector switch) while only the bridge was available from the treble output jack. Since it was about a week ago when I did the test and my original note of only neck was coming from the DS-5R bass output was crossed out and replaced with either bridge or neck, I'm now not sure and think I need to repeat and confirm before saying definitively.
-Jon