Does a shielded cable provide any shielding if the shield isn't grounded? Would it be practically different than an unshielded cable?
Acting as a faraday cage, an ungrounded shield covering a twisted-pair will be somewhat effective. When in the presense of an interfering electric field, both wires in the twisted-pair are influenced more similarly than without the ungrounded shield and, this means that if the input stage that receives the signal has a decent common mode rejection figure, then that shield has some effectivity but, there are much more gains to be made by grounding that shield at the input amplifier end (even if it means connecting to ground via a relatively low valued capacitor like 10 nF).
Grounding at both ends can make things worse in terms of earth fault currents being passed up the shield.
As with any shield used to reduce noise, balanced drive and termination resistors are vital to maintain lowest CMRR.