First off, the noise on the thermistor wires will be from the drive AND from the current carrying conductors from the motor leads. I am sure if the drive is decent it has filtering to some degree. However, given that noise should be suppressed as close to the origination as possible to shunt it before it reaches larger levels (tends to happen with noise as it propagates along a wire), relying on the design of the drive to handle this is simply not a good idea. Many cheap drives are made these days and some will have no filtering. Heck, I even seen a drive that measured the current using an averaging scheme and a shunt internal to the drive. What were they thinking when they did this? The numbers they displayed for current where on average 15% off. So do not rely on the drive.
If the cable is armored this will help reduce coupling between the thermistor wire and the motor leads. Ideally this would be avoided although it is commonly done. If the motor leads were not armored I would avoid it for sure.
No matter if your using thermistors, RTD's, thermocouples or whatever, they are all generally very low voltage signals (depending on the driving voltage) so any noise affects these signals. The thermistor still needs to have a current through it to get a measurement of resistance to some measuring device.
I am sure this would not be a violation of the NEC since it is technically used by the same piece of equipment/circuit. But then the NEC is a safety code not a best practices code.