I'm having an electrician fish an Ethernet cable through a wall. I can put shielded or unshielded cat6. However, the electrician doesn't know how to crimp Ethernet cable so I agreed to do that part myself, and I only have materials on hand and experience for plastic crimps. Thus if I put shielded cable, the shield will be left floating. Can a floating shield potentially have worse characteristics than an unshielded cable?
Usually the cable goes to patch panel where you wrap the shield wire on the metal case that is grounded. The other end goes to metal socket and similarly the shield is connected on metal case. If you don't connect the shield, then there is no benefit using FTP over UTP
If the shield is not grounded, at least at one end, it is not really a shield so much as a wall, and noise can get around walls.
Worse, an ungrounded shield becomes an antenna that will resonate at a frequency that is dictated by the length and geometry of the wire.
That frequency will of course be nicely transferred to your signal lines.
So yes, ungrounded shield can make things worse.