What is the effect on noise immunity of a floating shield on a shielded twisted pair
Well, I gotta rush but https://www.dataforth.com/catalog/pdf/an507.pdf answers your question qualitatively


  Cable shielding is used primarily to minimize or eliminate capacitively coupled
  interference from electric fields. When properly implemented, it can also be used
  to minimize inductive coupling from magnetic fields. Shielding is only effective
  against electric fields if it provides a low impedance path to ground. A floating
  shield provides no protection against interference. Grounding of shields can be
  a controversial subject because there are several ways to do it. The correct
  place to connect an electrostatic shield is at the reference potential of the circuitry
  contained within the shield. This point will vary depending upon whether the
  source and receiver are both grounded or whether one or the other is floating.


Quantitatively, i.e. how much worse/better... hopefully someone else will answer.