The pitch shifter can't handle complex chords very well, it's more of an old fashioned pitch algorithm than a modern whammy or POG, so simple answer is no, it won't do that.
the added string noise from Dry mode prob comes from the sustain knob becoming a compressor threshold setting, bring the sustain control down in dry mode to back off the compression.
Plus i must say why not use a Bass Whammy for that pitchshifting?